Mixed Boundary Value Problems for non-Divergence Type Elliptic Equations in Unbounded Domain
Year: 2018
Type: preprint
Abstract: We investigate the qualitative properties of solution to the Zaremba type problem in unbounded domain for the non-divergence elliptic equation with possible degeneration at infinity. The main result is Phragmén-Lindelöf type principle on growth/decay of a solution at infinity depending on both the structure of the Neumann portion of the boundary and the "thickness" of its Dirichlet portion. The result is formulated in terms of so-called $s$-capacity of the Dirichlet portion of the boundary, while the Neumann boundary should satisfy certain "admissibility" condition in the sequence of layers converging to infinity.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2781689958