Year: 2025
Type: article
Abstract: We investigate the behavior of solutions of second-order elliptic Dirichlet problems for a convex domain by using a “gliding hump” technique and prove that there are no contour limits at a specified point of the boundary of the domain. Then we consider two-dimensional domains which have a reentrant (i.e., nonconvex) corner at a point P of the boundary of the domain. Assuming certain comparison functions exist, we prove that for any solution of an appropriate Dirichlet problem on the domain whose graph has finite area, there are infinitely many curves of finite length in the domain ending at P along which the solution has a limit at P. We then prove that such behavior occurs for quasilinear operations with positive genre.
Source: Axioms
Authors: Ammar Khanfer, Kirk Eugene Lancaster
Institution: Prince Sultan University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4410898723