Mixed Boundary Value Problems for non-Divergence Type Elliptic Equations in Unbounded Domain
Analysis of PDEs
2018-01-03 v1
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 Phragm\'en-Lindel\"of 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 -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.
Cite
@article{arxiv.1801.00741,
title = {Mixed Boundary Value Problems for non-Divergence Type Elliptic Equations in Unbounded Domain},
author = {Dat Cao and Akif Ibraguimov and Alexander I. Nazarov},
journal= {arXiv preprint arXiv:1801.00741},
year = {2018}
}