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We study regularity properties of the free boundary for the thin one-phase problem which consists of minimizing the energy functional $E (u, Ω) = \int_{Ω} {| \nabla u |}^{2} d X + ℋ^{n} ({u > 0} \cap {x_{n + 1} = 0}), Ω \subset ℝ^{n + 1},$ among all functions $u \geq 0$ which are fixed on $\partial Ω$ .

Regularity of minimal boundaries with obstacles

E. Barozzi, U. Massari (1982)

Rendiconti del Seminario Matematico della Università di Padova

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

Tanguy Briancon (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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.

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

Tanguy Briancon (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we prove some regularity results for the boundary of an open subset of $^{d}$ 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.

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Recent results in the approximation of free boundaries

Regularity and free boundary regularity for the $p$ Laplacian in Lipschitz and $C^{1}$ domains.

Regularity at the free boundary of two-dimensional stationary harmonic maps

Regularity in elliptic free boundary problems. II. Equations of higher order

Regularity in Parabolic Phase Transition Problems.

Regularity of a free boundary with application to the Pompeiu problem.

Regularity of a Minimal Surface at its Free Boundary.

Regularity of free boundaries in two dimensions

Regularity of Lipschitz free boundaries for the thin one-phase problem

Regularity of minimal boundaries with obstacles

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

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

Regularity of the free boundary for non degenerate phase transition problems of parabolic type

Regularity of the Poisson kernel and free boundary problems

Revisited isoperimetric inequalities for the p-capacity and application to the muskat problem

Risultati di regolarità, stabilità, instabilità e biforcazione per un problema a frontiera libera

Currently displaying 1 – 16 of 16