M. Allen

activity

20122023

most citedA Parabolic Problem with a Fractional-Time Derivative

160 citations · 192 across the 13 of their papers we have counts for

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Showing 2012Show all

2 papers · 1 filter

math.AP2012

The two-phase fractional obstacle problem

Mark Allen, Erik Lindgren, Arshak Petrosyan

We study minimizers of the functional $\int_{B_{1}^{+}} ∣\nabla u ∣^{2} x_{n}^{a} d x + 2 \int_{B_{1}^{'}} (λ_{+} u^{+} + λ_{-} u^{-}) d x^{'},$ for $a \in (- 1, 1)$ . The problem arises in connection with heat…

math.AP2012

Separation of a Lower Dimensional Free Boundary in a Two Phase Problem

Mark Allen

This paper studies local properties of a two phase free boundary problem for the fractional Laplacian. The main result states that the two free boundaries of the positive and negat…