Regularity of Lipschitz free boundaries in two-phase problems for the p-Laplace operator

• In this paper we study the regularity of the free boundary in a general two-phase free boundary problem for the p-Laplace operator and we prove, in particular, that Lipschitz free boundaries are C(1,gamma)-smooth for some gamma is an element of (0, 1). As part of our argument, and which is of independent interest, we establish a Hopf boundary type principle for non-negative p-harmonic functions vanishing on a portion of the boundary of a Lipschitz domain.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

p-Harmonic function

Free boundary

Two-phase

Boundary Harnack inequality

Hopf boundary principle

p-Subharmonic

Subsolution

Lipschitz domain

Regularity

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