Displaying similar documents to “Regularity of the optimal shape for the first eigenvalue of the laplacian with volume and inclusion constraints”

Regularity of optimal shapes for the Dirichlet’s energy with volume constraint

Tanguy Briancon (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we prove some regularity results for the boundary of an open subset of ℝ d which minimizes the Dirichlet’s energy among all open subsets with prescribed volume. In particular we show that, when the volume constraint is “saturated”, the reduced boundary of the optimal shape (and even the whole boundary in dimension 2) is regular if the state function is nonnegative.

On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications

Lars Diening, Josef Málek, Mark Steinhauer (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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We study properties of Lipschitz truncations of Sobolev functions with constant and variable exponent. As non-trivial applications we use the Lipschitz truncations to provide a simplified proof of an existence result for incompressible power-law like fluids presented in [Frehse (2003) 1064–1083]. We also establish new existence results to a class of incompressible electro-rheological fluids.