6 problems

Let $v$ be a weight, let $Q$ be a non-negative definite symmetric matrix, and suppose that the Sobolev hypothesis holds for some $sigma>1$. Define … For data $f\in L^A(v;\Omega)$,…

Let $p\geq 2$ and let $p'=\frac{p}{p-1}$ be the Hölder conjugate exponent, so that … For functions with bounded $p$-Laplacian, optimal regularity conjecture. The optimal regularity…

Let $\Omega$ be a bounded domain and consider the degenerate elliptic Dirichlet problem in the setting of the paper, assuming only a Sobolev inequality with no Orlicz gain. Even wh…

Let the Baouendi–Grushin Sobolev inequality be the inequality denoted by, for parameters $m$, $n$, and $\alpha$, and let an extremal function mean a function attaining equality in…

Let $d\geq 1$ and let $\alpha\in(-1,\infty)$. Consider the corollary's hypotheses and conclusion for the boundary value problem in the half cylinder $Q_2^+$, with $p^*$ satisfying…

Let $u$ solve the degenerate Monge–Ampère equation … on $B_1$, where $f\in C^\infty(B_1)$ satisfies, for some constants $A>0$, $B\geq 0$ and positive integers $l\leq m$, … Assume t…