Optimal regularity in the lower dimensional obstacle problem with variable coefficients
Abstract
We study the interior Signorini, or lower-dimensional obstacle problem for a uniformly elliptic divergence form operator L = div( A(x)∇) with Lipschitz continuous coefficients. Our main result states that, similarly to what happens when L = Δ, the variational solution has the optimal interior regularity C1,1/2loc(Ω ± ∪ M), when M is a codimension one flat manifold which supports the obstacle. We achieve this by proving some new monotonicity formulas for an appropriate generalization of the celebrated Almgren's frequency functional.
Degree
Ph.D.
Advisors
Petrosyan, Purdue University.
Subject Area
Mathematics
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