Lipschitz continuity of state functions in some optimal shaping

Brian�on, Tanguy; Hayouni, Mohammed; Pierre, Michel
May 2005
Calculus of Variations & Partial Differential Equations;May2005, Vol. 23 Issue 1, p13
Academic Journal
We prove local Lipschitz continuity of the solution to the state equation in two kinds of shape optimization problems with constraint on the volume: the minimal shaping for the Dirichlet energy, with no sign condition on the state function, and the minimal shaping for the first eigenvalue of the Laplacian. This is a main first step for proving regularity of the optimal shapes themselves.


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