arXiv subjects
Publications and source records attributed to Somayeh Khademloo.
In the unit ball, we study a semilinear system that gives rise to a free boundary of Alt-Phillips type, where the equation is governed by a mixed variable-exponent operator of $(p,q)$-Laplacian type. Under certain structural conditions, we establish the existence of nonnegative radial solutions that are $C^1$, with their norms depending on the structural data.
Given $Ω\subset \mathbb{R}^n$ with $n\geq 2$, $D\subset Ω$ open, and $u:Ω\to \mathbb{R}^m$, we study elliptic systems of the type $$ {\rm div} \big( ( A + (B- A)χ_D)\nabla u\big) = 0 \quad \text{in $Ω\cap B_1$,} $$ for some uniformly elliptic tensors $A$ and $B$ with Hölder continuous entries. We show that, given appropriate boundary data, the Lipschitz regularity of $u$ inside $B_1 \cap D$ is transmitted to $B_{1/2}\cap Ω$ up to the boundary of $Ω$. This corresponds to the boundary counterpart of the interior regularity results in Figalli-Kim-Shahgholian, Nonlinear Anal. 2022.