Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the $p(x)$-Laplacian

NOEMI WOLANSKI; CLAUDIA LEDERMAN

INTERFACES AND FREE BOUNDARIES

EUROPEAN MATHEMATICAL SOC

Lugar: Zürich; Año: 2017 vol. 19 p. 201 - 241

1463-9963

In this paper we study a one phase  free boundaryproblem for the $p(x)$-Laplacian with non-zero right hand side.We  prove that the free boundary  of a weaksolution is a $C^{1,alpha}$ surface in a neighborhood of every``flat´´ free boundary point.We also obtain further regularity results on the free boundary,under further regularity assumptions on the data.We apply these results to limit functions of an inhomogeneoussingular perturbation problem for the $p(x)$-Laplacian that westudied in cite{LW4}.