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

Damian Wiśniewski

doi:10.1515/amsil-2016-0009

.blurhash-client-img { display: none !important; }

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

Annales Mathematicae Silesianae

Volume 30 (2016): Issue 1 (September 2016)

By: Damian Wiśniewski

Open Access

|Sep 2016

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.

References

[1] Borsuk M.V., Transmission problems for elliptic second-order equations in non-smooth domains, Birkhäuser, Basel, 2010.10.1007/978-3-0346-0477-2
Search in Google Scholar Back to article
[2] Hernández J., Mancebo F.J., Vega J.M., On the linearization of some singular, nonlinear elliptic problems and applications, Ann. Inst. H. Poincaré Anal. Non Linéaire 19 (2002), 777–813.10.1016/s0294-1449(02)00102-6
Search in Google Scholar Back to article
[3] Lazer A.C., McKenna P.J., On a singular nonlinear elliptic boundary-value problem, Proc. Amer. Math. Soc. 111 (1991), 721–730.10.1090/S0002-9939-1991-1037213-9
Search in Google Scholar Back to article
[4] Mityushev V., Adler P., Darcy flow around a two-dimensional lens, I. Phys. A: Math. Gen. 39 (2006), 3545–3560.10.1088/0305-4470/39/14/004
Search in Google Scholar Back to article
[5] Murray J.D., Mathematical Biology, Springer, Berlin, 1993.10.1007/978-3-662-08542-4
Search in Google Scholar Back to article
[6] Nachman A., Callegari A., A nonlinear singular boundary value problem in the theory of pseudoplastic fluids, SIAM J. Appl. Math. 38 (1980), 275–281.10.1137/0138024
Search in Google Scholar Back to article
[7] Okubo A., Levin S.A., Diffusion and Ecological Problems: Modern Prospectives, Springer, New York, 2001.10.1007/978-1-4757-4978-6
Search in Google Scholar Back to article
[8] Wiśniewski D., Boundary value problems for a second-order elliptic equation in unbounded domains, Ann. Univ. Paed. Cracov. Studia Math. 9 (2010), 87–122.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/amsil-2016-0009 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

Journal RSS Feed

Language: English

Page range: 203 - 217

Submitted on: Feb 24, 2016

Accepted on: May 27, 2016

Published on: Sep 23, 2016

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

boundary value problems,

weak solutions,

second order elliptic linear equations,

Related subjects:

© 2016 Damian Wiśniewski, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 30 (2016): Issue 1 (September 2016)