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Adam Kubica (2005)
Applicationes Mathematicae
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We examine the regularity of weak and very weak solutions of the Poisson equation on polygonal domains with data in L². We consider mixed Dirichlet, Neumann and Robin boundary conditions. We also describe the singular part of weak and very weak solutions.
Damian Wiśniewski (2016)
Annales Mathematicae Silesianae
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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.
Urve Kangro, Roy Nicolaides (1999)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Clark, H.R., Ferrel, J.L., Clark, M.R. (2003)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Dien Hien Tran (1986)
Aplikace matematiky
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The process of gas exhalations in the lower layer of the atmosphere and the problem of distribution of new sources of exhalations in a hilly terrain are studied. Among other, the following assumptions are introduced: (1) the terrain is a hilly one, (2) the exhalations enter a chemical reaction with the atmosphere, (3) the process is stationary, (4) the vector of wind velocity satisfies the continuity equation. The mathematical formulation of the problem then is a mixed boundary value...
Dagmar Medková (2005)
Czechoslovak Mathematical Journal
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A necessary and sufficient condition for the boundedness of a solution of the third problem for the Laplace equation is given. As an application a similar result is given for the third problem for the Poisson equation on domains with Lipschitz boundary.
Marco Cannone, Changxing Miao, Nicolas Prioux, Baoquan Yuan (2006)
Banach Center Publications
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We study the uniqueness and regularity of Leray-Hopf's weak solutions for the MHD equations with dissipation and resistance in different frameworks. Using different kinds of space-time estimates in conjunction with the Littlewood-Paley-Bony decomposition, we present some general criteria of uniqueness and regularity of weak solutions to the MHD system, and prove the uniqueness and regularity criterion in the framework of mixed space-time Besov spaces by applying Tao's trichotomy method. ...
Weihua Geng (2015)
Molecular Based Mathematical Biology
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Numerically solving the Poisson-Boltzmann equation is a challenging task due to the existence of the dielectric interface, singular partial charges representing the biomolecule, discontinuity of the electrostatic field, infinite simulation domains, etc. Boundary integral formulation of the Poisson-Boltzmann equation can circumvent these numerical challenges and meanwhile conveniently use the fast numerical algorithms and the latest high performance computers to achieve combined improvement...
Tber, Moulay Hicham (2007)
APPS. Applied Sciences
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