Cavity type problems ruled by infinity Laplacian operator
Copyright policy )Cavity type problems ruled by infinity Laplacian operator
We study a singularly perturbed problem related to infinity Laplacian operator with prescribed boundary values in a region. We prove that solutions are locally (uniformly) Lipschitz continuous, they grow as a linear function, are strongly non-degenerate and have porous level surfaces. Moreover, for some restricted cases we show the finiteness of the (n-1)-dimensional Hausdorff measure of level sets. The analysis of the asymptotic limits is carried out as well.
22 pages
- University of Buenos Aires Argentina
- University of Coimbra Portugal
- National Scientific and Technical Research Council Argentina
- Universidade Federal do Ceará Brazil
Smoothness and regularity of solutions to PDEs, Hausdorff Measure, Nonlinear elliptic equations, Lipschitz Regularity, Hausdorff measure, Viscosity solutions to PDEs, Mathematics - Analysis of PDEs, Boundary value problems for higher-order elliptic equations, FOS: Mathematics, Infinity Laplacian, https://purl.org/becyt/ford/1.1, Singular elliptic equations, Free boundary problems for PDEs, singularly perturbed problems, Lipschitz regularity, https://purl.org/becyt/ford/1, infinity Laplacian, Singularly Perturbed Problems, Analysis of PDEs (math.AP)
Smoothness and regularity of solutions to PDEs, Hausdorff Measure, Nonlinear elliptic equations, Lipschitz Regularity, Hausdorff measure, Viscosity solutions to PDEs, Mathematics - Analysis of PDEs, Boundary value problems for higher-order elliptic equations, FOS: Mathematics, Infinity Laplacian, https://purl.org/becyt/ford/1.1, Singular elliptic equations, Free boundary problems for PDEs, singularly perturbed problems, Lipschitz regularity, https://purl.org/becyt/ford/1, infinity Laplacian, Singularly Perturbed Problems, Analysis of PDEs (math.AP)
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