Calculus of Variations and Geometric Measure Theory

L. MalĂ˝ - N. Shanmugalingam

Neumann problem for p-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity

created by shanmugal on 23 Sep 2016
modified on 19 Jun 2018


Published Paper

Inserted: 23 sep 2016
Last Updated: 19 jun 2018

Journal: J. Diff. Eq.
Volume: 265
Number: 6
Pages: 2431-2460
Year: 2018


We employ a variational approach to study the Neumann boundary value problem for the $p$-Laplacian on bounded smooth-enough domains in the metric setting, and show that solutions exist and are bounded. The boundary data considered are Borel measurable bounded functions. We also study boundary continuity properties of the solutions. One of the key tools utilized is the trace theorem for Newton-Sobolev functions, and another is an analog of the De Giorgi inequality adapted to the Neumann problem.