<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

The Behaviour of Weak Solutions of Boundary Value Problems for Linear Elliptic Second Order Equations in Unbounded Cone-Like Domains

Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, Sloneczna 54, 10-710 Olsztyn,

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We investigate the behaviour of weak solutions of boundary value problems (Dirichlet, Neumann, Robin and mixed) for linear elliptic divergence second order...

The Behaviour of Weak Solutions of Boundary Value Problems for Linear Elliptic Second Order Equations in Unbounded Cone-Like Domains

Publié en ligne: 23 sept. 2016

Pages: 203 - 217

Reçu: 24 févr. 2016

Accepté: 27 mai 2016

DOI: https://doi.org/10.1515/amsil-2016-0009

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

© 2016 Damian Wiśniewski, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The Behaviour of Weak Solutions of Boundary Value Problems for Linear Elliptic Second Order Equations in Unbounded Cone-Like Domains

Publié en ligne: 23 sept. 2016

Pages: 203 - 217

Reçu: 24 févr. 2016

Accepté: 27 mai 2016

DOI: https://doi.org/10.1515/amsil-2016-0009

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

© 2016 Damian Wiśniewski, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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