Fine boundary regularity for fully nonlinear mixed local-nonlocal problems
Dr Abhrojyoti Sen ( IISER Pune )
| Speaker |
Dr Abhrojyoti Sen ( IISER Pune )
|
|---|---|
| When |
May 19, 2023
from 04:00 PM to 05:00 PM |
| Where | Via Zoom |
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Abstract: In this talk, we will consider Dirichlet problems for fully nonlinear mixed local-nonlocal non-translation invariant operators. For a bounded $C^2$ domain $\Omega \subset \mathbb{R}^d,$ let $u\in C(\mathbb{R}^d)$ be a viscosity solution of such Dirichlet problem. We discuss the global Lipschitz regularity and fine boundary regularity for $u$ by constructing appropriate sub and supersolutions coupled with a "weak version" of Harnack inequality. Moreover, applying these results we will discuss the H\"{o}lder regularity of $Du$ up to the boundary. We conclude the talk with some ongoing and future works.