Viscosity solutions to nonlocal generalized p-Laplacian: existence, uniqueness, and regularity


Oza P. Suragan D.
November 2025Birkhauser

Nonlinear Differential Equations and Applications
2025#32Issue 6

This paper investigates a gradient-degenerate, nonlocal version of the generalized p-Laplacian introduced by Baravdish, Cheng, Svensson, and Åström 2020. A key feature of this operator is its degeneracy along the set of critical points, which prevents the application of standard comparison principles. We establish the existence and interior Lipschitz regularity of viscosity solutions by employing an adapted Ishii-Lions “doubling variables” technique. We also identify a setting in which uniqueness of solutions is proved.

Integro-PDE , Nonlocal elliptic equation , Variable exponents , Viscosity solutions

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Department of Mathematics, Nazarbayev University, 53 Kabanbay Batyr Ave, Astana, 010000, Kazakhstan

Department of Mathematics

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