We study a nonlinear generalization of a free boundary problem that arises in the context of thermal insulation. We consider two open sets Ω ⊆ A , and we search for an optimal A in order to minimize a nonlinear energy functional, whose minimizers u satisfy the following conditions: Δ pu= 0 inside A\ Ω , u= 1 in Ω , and a nonlinear Robin-like boundary (p, q)-condition on the free boundary ∂A . We study the variational formulation of the problem in SBV , and we prove that, under suitable conditions on the exponents p and q, a minimizer exists and its jump set satisfies uniform density estimates.
A free boundary problem for the p-Laplacian with nonlinear boundary conditions
Acampora P.;
2024-01-01
Abstract
We study a nonlinear generalization of a free boundary problem that arises in the context of thermal insulation. We consider two open sets Ω ⊆ A , and we search for an optimal A in order to minimize a nonlinear energy functional, whose minimizers u satisfy the following conditions: Δ pu= 0 inside A\ Ω , u= 1 in Ω , and a nonlinear Robin-like boundary (p, q)-condition on the free boundary ∂A . We study the variational formulation of the problem in SBV , and we prove that, under suitable conditions on the exponents p and q, a minimizer exists and its jump set satisfies uniform density estimates.File in questo prodotto:
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