Variational inequalities for the fractional Laplacian

DOI10.1007/s11118-016-9591-9zbMath1368.35142arXiv1511.07417OpenAlexW2963223700MaRDI QIDQ525071

Roberta Musina, Alexander I. Nazarov, Konijeti Sreenadh

Publication date: 28 April 2017

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.07417

zbMATH Keywords

variational inequalitiesfree boundary problemsfractional Laplacian

Mathematics Subject Classification ID

Variational inequalities (49J40) Fractional partial differential equations (35R11) Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators (35J86) Unilateral problems for elliptic systems and systems of variational inequalities with elliptic operators (35J88)

Related Items (7)

The obstacle problem for nonlinear integro-differential operators ⋮ The Lewy-Stampacchia inequality for the fractional Laplacian and its application to anomalous unidirectional diffusion equations ⋮ On a class of nonlocal obstacle type problems related to the distributional Riesz fractional derivative ⋮ Finite element approximation of an obstacle problem for a class of integro–differential operators ⋮ Regularity analyses and approximation of nonlocal variational equality and inequality problems ⋮ Linear and nonlinear fractional elliptic problems ⋮ Almost minimizers for certain fractional variational problems

Cites Work

• Unnamed Item
• Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators
• Optimal regularity of solutions to the obstacle problem for the fractional Laplacian with drift
• Interior regularity of solutions of non-local equations in Sobolev and Nikol'skii spaces
• Monotone (nonlinear) operators in Hilbert space
• On the Sobolev and Hardy constants for the fractional Navier Laplacian
• \(H^s\) versus \(C^0\)-weighted minimizers
• Variational inequalities for the spectral fractional Laplacian
• Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem
• The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
• The extremal solution for the fractional Laplacian
• On the smoothness of superharmonics which solve a minimum problem
• Regularity of solutions to the parabolic fractional obstacle problem
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Regularity of solutions of variational inequalities
• An Introduction to Variational Inequalities and Their Applications
• Global regularity for the free boundary in the obstacle problem for the fractional Laplacian
• An Extension Problem Related to the Fractional Laplacian
• Sur la régularité de la solution d'inéquations elliptiques
• On the regularity of the solution of a variational inequality

This page was built for publication: Variational inequalities for the fractional Laplacian