{"id":82,"date":"2017-04-27T15:23:44","date_gmt":"2017-04-27T06:23:44","guid":{"rendered":"http:\/\/192.168.99.111\/dkim\/?p=82"},"modified":"2023-10-24T23:43:54","modified_gmt":"2023-10-24T14:43:54","slug":"test-page","status":"publish","type":"post","link":"https:\/\/mathematicians.korea.ac.kr\/dkim\/2017\/04\/27\/test-page\/","title":{"rendered":"Parabolic equations with measurable coefficients in $\\mathbb{R} \\times \\mathbb{R}^2$"},"content":{"rendered":"

Consider<\/p>\n

  <\/span>   <\/span>\"\[\left(a^{11}+a^{22}\right)u_t - \sum_{i,j=1}^2 a^{ij}(t,x_1,x_2) D_{ij}u = f,\]\"<\/p>\n

where \"a^{ij}(t,x_1,x_2)\" are measurable in \"(t,x_1,x_2)\" and \"a^{11}+a^{22}\" is measurable in \"t\", but constant in \"x \in \mathbb{R}^d\".<\/p>\n

Set<\/p>\n

  <\/span>   <\/span>\"\[\left[u_{ij}\right]<\/p>\n

We use the inequality<\/p>\n

  <\/span>   <\/span>\"\[\frac{1}{2\mu^2} \left( \sum a^{ij} u_{ij} \right)^2<\/p>\n","protected":false},"excerpt":{"rendered":"

Consider     where are measurable in and is measurable in , but constant in . Set     We use the inequality    <\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-82","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"distributor_meta":false,"distributor_terms":false,"distributor_media":false,"distributor_original_site_name":"Homepage for Doyoon Kim","distributor_original_site_url":"https:\/\/mathematicians.korea.ac.kr\/dkim","push-errors":false,"_links":{"self":[{"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/posts\/82","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/comments?post=82"}],"version-history":[{"count":7,"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/posts\/82\/revisions"}],"predecessor-version":[{"id":204,"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/posts\/82\/revisions\/204"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/media?parent=82"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/categories?post=82"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/dkim\/wp-json\/wp\/v2\/tags?post=82"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}