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Let $D_1$ and $D_2$ be two bounded simply connected Jordan domains in $\mathbb{R}^2$. By Carathéodory's Theorem there exists a homeomorphism $f:\bar{D}_1 \to \bar{D}_2$ such that the restriction $f:...

This is a question on a degenerate elliptic operator. Let $E$ be a closed unit ball in $\mathbb{R}^d$ centered at the origin. For a positive number $c>0$ and $f \in C^2(E)(:=C^2(\mathbb{R}^d)|_E)$, ...

This soft/reference question is related to this MO post of a similar nature. What are some examples of elliptic PDEs appearing in control and BSDEs?

I am wondering if there is any literature on the relationship between diffusions and elliptic equations. In particular I am interested in literature concerning operators with Dahlberg–Kenig–Pipher ...

The link between the Brownian motion and the Laplace operator is well-known. What stochastic process plays an analogous role with respect to the $p$-Laplace operator?