In the last nonlinear analysis seminar, Professor Espinar talked about the overdetermined elliptic problem(OEP) which looks like the following

There is a BCN conjecture related to this… 88 more words

In the last nonlinear analysis seminar, Professor Espinar talked about the overdetermined elliptic problem(OEP) which looks like the following

There is a BCN conjecture related to this… 88 more words

We will show a basic argument why Harnack inequality implies Holder continuity. Assume is a weak solution to a uniform elliptic equation

in . Assume we have Harnack inequality (Indeed we do have due to Moser), i.e. 83 more words

— 1. Definition of Newtonian Potential —

882 more wordsDefinition 1 Let be a bounded open set, we define the Newtonian potential of is the function on by…