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Neumann problems and isocapacitary inequalities
Dipartimento di Matematica e Applicazioni per l'Architettura, Università di Firenze, Piazza Ghiberti 27, 50122 Firenze, Italy.
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
2008 (English)In: Journal des Mathématiques Pures et Appliquées, ISSN 0021-7824, Vol. 89, no 1, 71-105 p.Article in journal (Refereed) Published
Abstract [en]

A priori bounds for solutions to (nonlinear) elliptic Neumann problems in open subsets O of Rn are established via inequalities relating the Lebesgue measure of subsets of O to their relative capacity. Both norm and capacitary estimates for solutions, and norm estimates for their gradients are derived which improve classical results even in the case of the Laplace equation. © 2007 Elsevier Masson SAS. All rights reserved.

Place, publisher, year, edition, pages
2008. Vol. 89, no 1, 71-105 p.
Keyword [en]
A priori estimates, Capacity, Elliptic equations, Rearrangements
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-47288DOI: 10.1016/j.matpur.2007.10.001OAI: diva2:268184
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-11

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Maz´ya, Vladimir G.
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