Regularity results of solutions to elliptic equations involving mixed local and nonlocal operators

In this paper, we study the summability of solutions to the following semilinear elliptic equations involving mixed local and nonlocal operators {-Delta u(x) + (-Delta)(s)u(x) = f(x) , x is an element of Omega, u(x) >= 0, is an element of Omega, u(x) = 0 , x is an element of R-N\Omega, where 0 < s < 1, Omega subset of R-N is a smooth bounded domain, (-Delta)(s) is the fractional Laplace operator, f is a measurable function.

Automated summary

In this paper, the summability of solutions to a class of semilinear elliptic equations involving mixed local and nonlocal operators is studied. The equations are defined on a smooth bounded domain Ω, which is a subset of R-N.