Maurizio Chicco, Marina Venturino (2006)
Bollettino dell'Unione Matematica Italiana
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We prove Holder regularity for solutions of mixed boundary value problems for a class of divergence form elliptic equations with discontinuous and unbounded coefficients, in the presence of boundary integrals.
A. Azzam (1981)
Annales Polonici Mathematici
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E. Shamir (1963)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Konrad Gröger (1989)
Mathematische Annalen
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Chaohao Gu (1980)
Journées équations aux dérivées partielles
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Jan Brandts (1999)
Applications of Mathematics
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We will show that some of the superconvergence properties for the mixed finite element method for elliptic problems are preserved in the mixed semi-discretizations for a diffusion equation and for a Maxwell equation in two space dimensions. With the help of mixed elliptic projection we will present estimates global and pointwise in time. The results for the Maxwell equations form an extension of existing results. For both problems, our results imply that post-processing and a posteriori...
Daniele Castorina, Gianni Mancini (2003)
Rendiconti del Seminario Matematico della Università di Padova
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Pierre-Emmanuel Jabin, Felix Otto, BenoÎt Perthame (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states of vanishing energy. We classify these zero-energy states in the whole space: They are either constant or a vortex. A bounded domain can sustain a zero-energy state only if the domain is a disk and the state a vortex. Our proof is based on specific entropies which lead to a kinetic formulation, and...
H. Marcinkowska (1982)
Colloquium Mathematicae
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Mikhail Borsuk, Krzysztof Żyjewski (2011)
Applicationes Mathematicae
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We investigate the behavior of weak solutions to the nonlocal Robin problem for linear elliptic divergence second order equations in a neighborhood of a boundary corner point. We find an exponent of the solution's decreasing rate under minimal assumptions on the problem coefficients.