Mixed boundary value problems for non-divergence type elliptic equations in unbounded domains

Dat Cao, Akif Ibraguimov, Alexander I. Nazarov

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate the qualitative properties of solutions to the Zaremba type problem in unbounded domains for non-divergence elliptic equation with possible degeneration at infinity. The main result is a 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 the 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.

Original languageEnglish
Pages (from-to)75-90
Number of pages16
JournalAsymptotic Analysis
Volume109
Issue number1-2
DOIs
StatePublished - 2018

Keywords

  • Non-divergence elliptic equations
  • Phragmén-Lindelöf theorem
  • Zaremba type problem
  • growth lemma
  • mixed boundary value problems

Fingerprint Dive into the research topics of 'Mixed boundary value problems for non-divergence type elliptic equations in unbounded domains'. Together they form a unique fingerprint.

Cite this