Electron. J. Differential Equations, Vol. 2025 (2025), No. 51, pp. 1-30.

Neumann-Robin problem for p(x)-Laplacian equations in a domain with the boundary edge

Mikhail Borsuk

Abstract:
We investigate the behavior of weak solutions to the mixed problem with Neumann and Robin boundary conditions for an elliptic quasi-linear second-order equation with the variable \(p(x)\)-Laplacian in a neighborhood of the boundary edge.

Submitted January 20, 2025. Published May 24, 2025.
Math Subject Classifications: 35J20, 35J25, 35J70.
Key Words: p(x)-Laplacian; boundary edge; mixed problem; Neumann problem; Robin problem.
DOI: 10.58997/ejde.2025.51

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Mikhail Borsuk
Faculty of Mathematics and Computer Science
University of Warmia and Mazury in Olsztyn
10-957 Olsztyn-Kortowo, Poland
email: mborsuk40@gmail.com

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