{"id":326,"date":"2017-05-01T10:41:48","date_gmt":"2017-05-01T01:41:48","guid":{"rendered":"http:\/\/192.168.99.111\/kyeonghun\/?page_id=326"},"modified":"2017-09-01T16:18:35","modified_gmt":"2017-09-01T07:18:35","slug":"research-interest","status":"publish","type":"page","link":"https:\/\/mathematicians.korea.ac.kr\/kyeonghun\/research-interest\/","title":{"rendered":"Research Interest"},"content":{"rendered":"

 <\/p>\n

Stochastic Partial Differential Equations:<\/strong><\/p>\n

I have been working on the maximal \"L_p\" (or Sobolev)-regularity theory of SPDEs with the emphasis on the following:<\/p>\n

    \n
  1. Differential operators<\/strong>: 2nd-order operators, pseudo-differential operators, \u00a0infinitesimal generator of Levy process, and operators related to \u00a0anomalous diffusions.<\/li>\n
  2. Domains<\/strong>: \"C^1\"-domains, Lipschitz domains, angular domain and general non-smooth domains.<\/li>\n
  3. Coefficients<\/strong>: continuous leading coefficients, measurable leading coefficients, \u00a0unbounded leading coefficients, and degenerate equations.<\/li>\n
  4. Noises<\/strong>: Brownian motions, Levy noises, semi-martingales.<\/li>\n
  5. Some quasi-and semi-linear SPDEs<\/strong><\/li>\n<\/ol>\n

     <\/p>\n

    2nd-oder Linear PDEs<\/strong>:<\/p>\n

      \n
    1. \u00a0Discontinuous, degenerate and \u00a0unbounded leading coefficients.<\/li>\n
    2. Weighted \"L_p\"-regularity theory on non-smooth domains.<\/li>\n<\/ol>\n

       <\/p>\n

      PDE related to stochastic processes:<\/strong><\/p>\n

      I also have great interest in \"L_p\" and H\"\"o\"der regularity theory for PDEs whose differential operators are infinitesimal generator of stochastic processes such as Levy processes and non-stationary stochastic processes.<\/p>\n","protected":false},"excerpt":{"rendered":"

        Stochastic Partial Differential Equations: I have been working on the maximal (or Sobolev)-regularity theory of SPDEs with the emphasis on the following: Differential operators: 2nd-order operators, pseudo-differential operators, \u00a0infinitesimal generator of Levy process, and operators related to \u00a0anomalous diffusions. … \uacc4\uc18d \uc77d\uae30 →<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"ngg_post_thumbnail":0,"footnotes":""},"class_list":["post-326","page","type-page","status-publish","hentry"],"distributor_meta":false,"distributor_terms":false,"distributor_media":false,"distributor_original_site_name":"Kyeonghun Kim\u2019s homepage","distributor_original_site_url":"https:\/\/mathematicians.korea.ac.kr\/kyeonghun","push-errors":false,"_links":{"self":[{"href":"https:\/\/mathematicians.korea.ac.kr\/kyeonghun\/wp-json\/wp\/v2\/pages\/326","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematicians.korea.ac.kr\/kyeonghun\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mathematicians.korea.ac.kr\/kyeonghun\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/kyeonghun\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/kyeonghun\/wp-json\/wp\/v2\/comments?post=326"}],"version-history":[{"count":19,"href":"https:\/\/mathematicians.korea.ac.kr\/kyeonghun\/wp-json\/wp\/v2\/pages\/326\/revisions"}],"predecessor-version":[{"id":504,"href":"https:\/\/mathematicians.korea.ac.kr\/kyeonghun\/wp-json\/wp\/v2\/pages\/326\/revisions\/504"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/kyeonghun\/wp-json\/wp\/v2\/media?parent=326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}