Regularity of the Free Boundary for a Bernoulli-Type Parabolic Problem\n with Variable Coefficients

2015/12/02 by Thomas Backing, Backing, Thomas
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1512.00917

openalex publication_date 2015/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies the regularity of the free boundary for viscosity\nsolutions to a parabolic Bernoulli-type free boundary problem with variable\ncoefficients. The main result is that Lipschitz free boundaries are C¹ with\na normal vector that varies with a H "older modulus of continuity in both space\nand in time. As a consequence, the viscosity solution satisfies the free\nboundary problem in a classical sense.\n

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