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November 13, 2013

4:10PM - 5:05PM

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MW 154

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`2013-11-13 17:10:00``2013-11-13 18:05:00``New Developments in the Thin Obstacle Problem with Lipschitz Coefficients``Speaker: Mariana Smit Vega Garcia, Purdue UniversityAbstract: We will describe the lower-dimensional obstacle problem for a uniformly elliptic, divergence form operator L=div(A(x)∇) with Lipschitz continuous coefficients and discuss the optimal regularity of the solution. Our main result states that, similarly to what happens when L=Δ, the variational solution has the optimal interior regularity. We achieve this by proving some new monotonicity formulas for an appropriate generalization of Almgren's frequency functional.Seminar Website: http://people.mbi.ohio-state.edu/lam.184/pdeseminar/pdeseminar2012.html``MW 154``OSU ASC Drupal 8``ascwebservices@osu.edu``America/New_York``public`Date Range

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`2013-11-13 16:10:00``2013-11-13 17:05:00``New Developments in the Thin Obstacle Problem with Lipschitz Coefficients``Speaker: Mariana Smit Vega Garcia, Purdue UniversityAbstract: We will describe the lower-dimensional obstacle problem for a uniformly elliptic, divergence form operator L=div(A(x)∇) with Lipschitz continuous coefficients and discuss the optimal regularity of the solution. Our main result states that, similarly to what happens when L=Δ, the variational solution has the optimal interior regularity. We achieve this by proving some new monotonicity formulas for an appropriate generalization of Almgren's frequency functional.Seminar Website: http://people.mbi.ohio-state.edu/lam.184/pdeseminar/pdeseminar2012.html``MW 154``Department of Mathematics``math@osu.edu``America/New_York``public`Description

**Speaker**: **Mariana Smit Vega Garcia**, Purdue University

**Abstract**: We will describe the lower-dimensional obstacle problem for a uniformly elliptic, divergence form operator L=div(A(x)∇) with Lipschitz continuous coefficients and discuss the optimal regularity of the solution. Our main result states that, similarly to what happens when L=Δ, the variational solution has the optimal interior regularity. We achieve this by proving some new monotonicity formulas for an appropriate generalization of Almgren's frequency functional.

**Seminar Website:** http://people.mbi.ohio-state.edu/lam.184/pdeseminar/pdeseminar2012.html