Some remarks on the duality method for Integro-Differential equations with measure data

Abstract

We deal with existence, uniqueness, and regularity for solutions of the boundary value problem $$\{\begin{array}{llc}{\mathcal{L}}^{s}u=\mu & \text{in Ω},u(x)=0& \text{on}{\mathbb{R}}^N\backslash \Omega ,\end{array}$$ where $\Omega$ is a bounded domain of ${\mathbb{R}}^N$, $\mu$ is a bounded radon measure on $\Omega$, and ${\mathcal{L}}^s$ is a nonlocal operator of fractional order $s$ whose kernel $K$ is comparable with the one of the factional laplacian.

References in corpus (3)

• Inverse Problem for a Curved Quantum Guide
• Nonlocal equations with measure data
• On $L_p$-estimates for a class of non-local elliptic equations

Cited by in corpus (3)

• A fractional Laplacian problem with mixed singular nonlinearities and nonregular data
• A note on the existence of a unique positive entropy solution to a fractional Laplacian with singular nonlinearities
• On semilinear elliptic equations with diffuse measures