Neumann problems and isocapacitary inequalities

• 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.

Nyckelord

A priori estimates

Capacity

Elliptic equations

Rearrangements

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