{"id":18078,"date":"2023-10-24T09:53:38","date_gmt":"2023-10-24T01:53:38","guid":{"rendered":"https:\/\/cantor.math.ntnu.edu.tw\/?p=18078"},"modified":"2023-10-24T10:01:04","modified_gmt":"2023-10-24T02:01:04","slug":"lecture20231101","status":"publish","type":"post","link":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/2023\/10\/24\/lecture20231101\/","title":{"rendered":"<span style=\"color:#3566BD\">[\u5c08\u984c\u6f14\u8b1b] <\/span>\u301011\u67081\u65e5\u3011Kyung-Youn Kim \/ Potential theory of anisotropic Markov processes"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"18078\" class=\"elementor elementor-18078\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-19a5332c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"19a5332c\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-68eb95a1\" data-id=\"68eb95a1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4d878518 elementor-widget elementor-widget-heading\" data-id=\"4d878518\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Potential theory of anisotropic Markov processes<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-51461cf0 elementor-widget elementor-widget-spacer\" data-id=\"51461cf0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4ccaf3ea elementor-widget elementor-widget-text-editor\" data-id=\"4ccaf3ea\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"color: #000080; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: bold;\">\u6642\u3000\u9593\uff1a2023-11-01 14:00 (\u661f\u671f\u4e09) \/ \u5730\u3000\u9ede\uff1aS101 \/ \u8336\u3000\u6703\uff1aS205 (13:30)<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4940900d elementor-widget elementor-widget-image\" data-id=\"4940900d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"264\" height=\"270\" src=\"https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2023\/10\/1121101Kim.png\" class=\"attachment-full size-full wp-image-18080\" alt=\"\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-26032a62 elementor-widget elementor-widget-text-editor\" data-id=\"26032a62\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div style=\"list-style: none; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; margin-top: 10px; font-size: 22px; line-height: 26px; text-align: center; color: #cc6633; font-weight: bold;\">Kyung-Youn Kim \u91d1\u749f\u5141<\/div><div style=\"list-style: none; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; margin-top: 10px; font-size: 18px; line-height: 22px; text-align: center; color: #cc9966; font-weight: bold;\">\u570b\u7acb\u4e2d\u8208\u5927\u5b78 \u61c9\u7528\u6578\u5b78\u7cfb\u52a9\u7406\u6559\u6388<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5c79e75 elementor-widget elementor-widget-spacer\" data-id=\"5c79e75\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5fd7cb59 elementor-widget elementor-widget-text-editor\" data-id=\"5fd7cb59\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Heat kernel is the fundamental solution of the heat equation, and it is also the transition density of the diffusion process corresponding to the Laplacian. These relation is also ture for non-local operators, and corresponding process is a discontinuous Markov process. In this talk, we consider anisotropic Markov processes. Let <span class=\"katex\"><span class=\"katex-mathml\"><math><semantics><mrow><msub><mi>L<\/mi><mi>i<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">L_i<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, <span class=\"katex\"><span class=\"katex-mathml\"><math><semantics><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mo>\u2026<\/mo><mo separator=\"true\">,<\/mo><mi>d<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">i=1,\\ldots,d<\/annotation><\/semantics><\/math><\/span><\/span>, be identical and independent <span class=\"katex\"><span class=\"katex-mathml\"><math><semantics><mrow><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">1<\/annotation><\/semantics><\/math><\/span><\/span>-dimensional L\\&#8217;evy processes. Define a Markov process <span class=\"katex\"><span class=\"katex-mathml\"><math><semantics><mrow><mi>M<\/mi><mo>:<\/mo><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><msub><mi>M<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mo>\u2026<\/mo><mo separator=\"true\">,<\/mo><msub><mi>M<\/mi><mi>d<\/mi><\/msub><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">M:=(M_1, \\ldots, M_d)<\/annotation><\/semantics><\/math><\/span><\/span> whose jumping kernel is comparable to that of <span class=\"katex\"><span class=\"katex-mathml\"><math><semantics><mrow><mi>L<\/mi><mo>:<\/mo><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><msub><mi>L<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mo>\u2026<\/mo><mo separator=\"true\">,<\/mo><msub><mi>L<\/mi><mi>d<\/mi><\/msub><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">L:=(L_1, \\ldots, L_d)<\/annotation><\/semantics><\/math><\/span><\/span>. Then <span class=\"katex\"><span class=\"katex-mathml\"><math><semantics><mrow><mi>M<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">M<\/annotation><\/semantics><\/math><\/span><\/span> is a pure jump process that jumps parallel to the coordinate axes. We discuss the sharp two-sided heat kernel bounds for <span class=\"katex\"><span class=\"katex-mathml\"><math><semantics><mrow><mi>M<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">M<\/annotation><\/semantics><\/math><\/span><\/span> on <span class=\"katex\"><span class=\"katex-mathml\"><math><semantics><mrow><msup><mi>C<\/mi><mrow><mn>1<\/mn><mo separator=\"true\">,<\/mo><mn>1<\/mn><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">C^{1,1}<\/annotation><\/semantics><\/math><\/span><\/span> open set <span class=\"katex\"><span class=\"katex-mathml\"><math><semantics><mrow><mi>D<\/mi><mo>\u2282<\/mo><msup><mrow><mi mathvariant=\"normal\">I<\/mi>\u2009\u2063<mi mathvariant=\"normal\">R<\/mi><\/mrow><mi>d<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">D\\subset {\\rm I\\!R}^d<\/annotation><\/semantics><\/math><\/span><\/span> as well as the potential theory of anisotropic Markov process. This is the joint work with Lidan Wang.<\/p><p>[1] Dirichlet Heat kernel estimates for a large class of anisotropic Markov process (with Lidan Wang).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-76d951d3 elementor-widget elementor-widget-image\" data-id=\"76d951d3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1240\" height=\"758\" src=\"https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e.jpg\" class=\"attachment-full size-full wp-image-7367\" alt=\"\" srcset=\"https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e.jpg 1240w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e-300x183.jpg 300w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e-768x469.jpg 768w, https:\/\/cantor.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e-1024x626.jpg 1024w\" sizes=\"(max-width: 1240px) 100vw, 1240px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Potential theory of anisotropic Markov processes \u6642\u3000\u9593\uff1a20 [&hellip;]<\/p>\n","protected":false},"author":23,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"","ocean_second_sidebar":"","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"","ocean_custom_header_template":"","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"","ocean_menu_typo_font_family":"","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"","ocean_post_oembed":"","ocean_post_self_hosted_media":"","ocean_post_video_embed":"","ocean_link_format":"","ocean_link_format_target":"self","ocean_quote_format":"","ocean_quote_format_link":"post","ocean_gallery_link_images":"off","ocean_gallery_id":[],"footnotes":""},"categories":[1,124],"tags":[],"class_list":["post-18078","post","type-post","status-publish","format-standard","hentry","category-news","category-speeches","entry"],"_links":{"self":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/18078","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/users\/23"}],"replies":[{"embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/comments?post=18078"}],"version-history":[{"count":14,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/18078\/revisions"}],"predecessor-version":[{"id":18103,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/18078\/revisions\/18103"}],"wp:attachment":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/media?parent=18078"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/categories?post=18078"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/tags?post=18078"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}