Subsolutions of Elliptic Operators in Divergence Form and Application to Two-Phase Free Boundary Problems
Fausto Ferrari, Sandro Salsa · Boundary Value Problems · 2006
Let be a divergence form operator with Lipschitz continuous coefficients in a domain , and let be a continuous weak solution of in . In this paper, we show that if satisfies a suitable differential inequality, then is a subsolution of away from its zero set. We apply this result to prove regularity of Lipschitz free boundaries in two-phase problems.