Quasi-monotonicity formulas for classical obstacle problems with Sobolev coefficients and applications

2018/06/08 by Matteo Focardi, Focardi, Matteo, Francesco Geraci +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Approximation and Integration #Nonlinear Partial Differential Equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1806.03179

openalex publication_date 2018/06/08 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We establish Weiss' and Monneau's type quasi-monotonicity formulas for quadratic energies having matrix of coefficients in a Sobolev space W^1,p, p>n, and provide an application to the corresponding free boundary analysis for the related classical obstacle problems.

Related

• Monotonicity formulas for obstacle problems with Lipschitz coefficients
• The Classical Obstacle problem with coefficients in fractional Sobolev spaces
• The classical obstacle problem with Hölder continuous coefficients
• On the free boundary for thin obstacle problems with Sobolev variable coefficients
• The classical obstacle problem for nonlinear variational energies