Optimal regularity and nondegeneracy of a free boundary problem related to the fractional Laplacian

2011/01/13 by Ray Yang, Yang, Ray · 1 citation
Computer Science · Mathematics · #35R35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1101.2601

openalex publication_date 2011/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the optimal regularity and nondegeneracy of a free boundary problem related to the fractional Laplacian. This work is related to, but addresses a different problem from, recent work of Caffarelli, Roquejoffre, and Sire. A variant of the boundary Harnack inequality is also proved, where it is no longer required that the function be 0 along the boundary.

Citations

• Potential methods in variational inequalities
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian

Cited by

• The free boundary for a superlinear system

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