Regularity results for solutions to obstacle problems with Sobolev coefficients

2020 ◽  
Vol 269 (10) ◽  
pp. 8308-8330
Author(s):  
Michele Caselli ◽  
Andrea Gentile ◽  
Raffaella Giova
Keyword(s):  
Obstacle Problems ◽  
Regularity Results

scholarly journals Boundary Regularity for p-Harmonic Functions and Solutions of Obstacle Problems on Unbounded Sets in Metric Spaces

2019 ◽  
Vol 7 (1) ◽  
pp. 179-196
Author(s):  
Anders Björn ◽  
Daniel Hansevi
Keyword(s):  
Harmonic Functions ◽  
Obstacle Problem ◽  
Metric Spaces ◽  
Local Property ◽  
Boundary Regularity ◽  
Obstacle Problems ◽  
Regular Boundary ◽  
Complete Metric Spaces ◽  
Regularity Results

Abstract The theory of boundary regularity for p-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a p-Poincaré inequality, 1 < p < ∞. The barrier classification of regular boundary points is established, and it is shown that regularity is a local property of the boundary. We also obtain boundary regularity results for solutions of the obstacle problem on open sets, and characterize regularity further in several other ways.

scholarly journals Regularity results for p-Laplacians in pre-fractal domains

2018 ◽  
Vol 8 (1) ◽  
pp. 1043-1056 ◽  
Author(s):  
Raffaela Capitanelli ◽  
Salvatore Fragapane ◽  
Maria Agostina Vivaldi
Keyword(s):  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Obstacle Problems ◽  
Convex Polygons ◽  
Regularity Results ◽  
Fractal Domains ◽  
Laplace Type

Abstract We study obstacle problems involving p-Laplace-type operators in non-convex polygons. We establish regularity results in terms of weighted Sobolev spaces. As applications, we obtain estimates for the FEM approximation for obstacle problems in pre-fractal Koch Islands.

scholarly journals Convergence rates for the classical, thin and fractional elliptic obstacle problems

2015 ◽  
Vol 373 (2050) ◽  
pp. 20140449 ◽  
Author(s):  
Ricardo H. Nochetto ◽  
Enrique Otárola ◽  
Abner J. Salgado
Keyword(s):  
Obstacle Problem ◽  
Fractional Laplacian ◽  
Convergence Rates ◽  
Finite Element Approximation ◽  
Obstacle Problems ◽  
Element Approximation ◽  
Optimal Error ◽  
Optimal Convergence Rates ◽  
Regularity Results ◽  
Thin Obstacle

We review the finite-element approximation of the classical obstacle problem in energy and max-norms and derive error estimates for both the solution and the free boundary. On the basis of recent regularity results, we present an optimal error analysis for the thin obstacle problem. Finally, we discuss the localization of the obstacle problem for the fractional Laplacian and prove quasi-optimal convergence rates.

Regularity results for a class of non-differentiable obstacle problems

2020 ◽  
Vol 194 ◽  
pp. 111434 ◽  
Author(s):  
Michela Eleuteri ◽  
Antonia Passarelli di Napoli
Keyword(s):  
Obstacle Problems ◽  
Regularity Results

Regularity of the Very Weak Solutions for Double Obstacle Problems

2010 ◽  
Vol 143-144 ◽  
pp. 1396-1400
Author(s):  
Xu Juan Xu ◽  
Xiao Na Lu ◽  
Yu Xia Tong
Keyword(s):  
Elliptic Equation ◽  
Weak Solutions ◽  
Minkowski Inequality ◽  
Young Inequality ◽  
Obstacle Problems ◽  
Very Weak Solutions ◽  
Local Integrability ◽  
Regularity Results ◽  
Harmonic Equation ◽  
Homogeneous Elliptic Equation

The apply of harmonic eauation is know to all. Our interesting is to get the regularity os their solution, recently for obstacle problems. Many interesting results have been obtained for the solutions of harmonic equation ande their obstacle problems, however the double obstacle problems about the definition and regularity results for non-homogeneous elliptic equation. In this paper , the basic tool for the Young inequality,Hölder inequality, Minkowski inequality, Poincaré inequality and a basic inequality. The definition of very weak solutions for double obstacle problems associated with non-homogeneous elliptic equation is given, and the local integrability result is obtained by using the technique of Hodge decomposition.

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