Neumann problem for p-Laplace equation in metric spaces using a variational approach: Existence, boundedness, and boundary regularity
Artikel i vetenskaplig tidskrift, 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.

Boundary regularity

Variational problem

De Giorgi type inequality

Neumann boundary value problem

p-Laplace equation

Metric measure space


Lukas Maly

University of Cincinnati

Nageswari Shanmugalingam

University of Cincinnati

Journal of Differential Equations

0022-0396 (ISSN) 1090-2732 (eISSN)

Vol. 265 2431-2460


Matematisk analys