The behaviour of weak solutions of boundary value problems for linear elliptic second order equations in unbounded cone-like domains

Damian Wiśniewski

Published: 2016-09-23

Vol. 30 (2016)

The behaviour of weak solutions of boundary value problems for linear elliptic second order equations in unbounded cone-like domains

Damian Wiśniewski

Abstract

We investigate the behaviour of weak solutions of boundary value problems (Dirichlet, Neumann, Robin and mixed) for linear elliptic divergence second order equations in domains extending to infinity along a cone. We find an exponent of the solution decreasing rate: we derive the estimate of the weak solution modulus for our problems near the infinity under assumption that leading coefficients of the equations do not satisfy the Dini-continuity condition.

Keywords:

boundary value problems , weak solutions , second order elliptic linear equations , unbounded domains , Dini-continuity

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Wiśniewski, D. (2016). The behaviour of weak solutions of boundary value problems for linear elliptic second order equations in unbounded cone-like domains. Annales Mathematicae Silesianae, 30, 203–217. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13965

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Vol. 30 (2016)
Published: 2016-09-23

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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