Elliptic 1-Laplacian equations with dynamical boundary conditions

Abstract

This paper is concerned with an evolution problem having an elliptic equation involving the 1-Laplacian operator and a dynamical boundary condition. We apply nonlinear semigroup theory to obtain existence and uniqueness results as well as a comparison principle. Our main theorem shows that the solution we found is actually a strong solution. We also compare solutions with different data.

Nonlocal diffusion equations with dynamical boundary conditions

“…Notice that dynamical boundary conditions have been studied by many authors. Among them, we mention: [11,12,13,14,15,16,17,21].…”