Full regularity of the free boundary in a Bernoulli-type problem in two dimensions
TLDR
In this paper, it was shown that in dimension n = 2 there are no singular points on the free boundary ∂{u > 0}∩Ω in the Bernoulli-type problem governed by the p-Laplace operator.Abstract:
In this note we prove that in dimension n = 2 there are no singular points on the free boundary ∂{u > 0}∩Ω in the Bernoulli-type problem governed by the p-Laplace operatorread more
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An optimization problem with volume constraint for a degenerate quasilinear operator
TL;DR: In this paper, the authors consider the optimization problem of minimizing ∫ Ω | ∇ u | p d x with a constraint on the volume of { u > 0 } and prove that for small values of the penalization parameter, the constrained volume is attained.
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An optimization problem with free boundary governed by a degenerate quasilinear operator
TL;DR: In this paper, the existence, regularity and geometrical properties of an optimal configuration to a free boundary optimization problem governed by the p-Laplacian operator were studied.
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An optimization problem with free boundary governed by a degenerate quasilinear operator
TL;DR: In this article, the existence, regularity and geometric properties of an optimal configuration to a free boundary optimization problem governed by the $p$-Laplacian were studied. And they were shown to be optimal.
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An optimization problem with volume constraint in Orlicz spaces
TL;DR: In this article, the authors considered the optimization problem of minimizing ∫ΩG(|∇u|)dx in the class of functions W1,G(Ω), with a constraint on the volume of {u>0}.
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Weak Solutions and Regularity of the Interface in an Inhomogeneous Free Boundary Problem for the p(x)-Laplacian
Claudia Lederman,Noemi Wolanski +1 more
TL;DR: In this article, the free boundary of a weak solution is shown to be a C^1 surface in a neighborhood of every free boundary point, under further regularity assumptions on the data, and they apply these results to limit functions of an inhomogeneous singular perturbation problem for the p(x)-Laplacian that they studied in Lederman, C., & Wolanski, N.
References
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Existence and regularity for a minimum problem with free boundary
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On harnack type inequalities and their application to quasilinear elliptic equations
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Regularity of the derivatives of solutions to certain degenerate elliptic equations
TL;DR: On montre que pour p fixe, 1
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TL;DR: In this article, the authors proved Cloc1,α estimates for solutions u ϵ W1,p + 2 of the degenerate elliptic p.d. div (¦Du¦ p Du) = 0 (p > 0).
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Partial regularity for a minimum problem with free boundary
TL;DR: The existence of singularities is equivalent to the existence of an absolute minimum u* such that the graph of u* is a cone with vertex at 0, the free boundary ∂{u* > 0} has one and only one singularity, and the set u* minimizes the perimeter among all its subsets as mentioned in this paper.