This paper is devoted to studying the blow-up and global existence of the solution to a
semilinear time-space fractional diffusion equation, where the time derivative is in the …

The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one-
phase free boundary problem. The problem of classifying stable (or minimal) homogeneous …

In this work, we study an elliptic problem involving an operator of mixed order with both local
and nonlocal aspects, and in either the presence or the absence of a singular nonlinearity …

This is a survey on the use of Fourier transformation methods in the treatment of boundary
problems for the fractional Laplacian $(-\Delta)^ a $(0< a< 1), and pseudodifferential …

In this article we establish fine results on the boundary behavior of solutions to nonlocal
equations in $ C^{k,\gamma} $ domains which satisfy local Neumann conditions on the …

For 2a-order strongly elliptic operators P generalizing (− Δ) a, 0< a< 1, the homogeneous
Dirichlet problem on a bounded open set Ω⊂ R n has been widely studied …

In this paper, we consider a class of integro-differential operators L posed on a C 2 bounded
domain Ω⊂ RN with appropriate homogeneous Dirichlet conditions where each of which …

We study the regularity of minimizers of the functional E (u):=[u] 2 Hs (Ω)+∫ Ω fu. This
corresponds to understanding solutions for the regional fractional Laplacian in Ω⊂ RN …

Semilinear equations for non-local operators: Beyond the fractional Laplacian - ScienceDirect
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In this article, we investigate the existence, uniqueness and regularity of weak solutions to
the following semilinear mixed local and nonlocal elliptic operators-Δ u+(-Δ) su= h (u) f, x∈ …