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Applied and Computational Math Seminar

Regularity and rate of approximation for obstacle problems for a class of integro-differential operators 

Abner Salgado, University of Tennessee, Knoxville 

Location:  Hill 525
Date & time: Friday, 02 November 2018 at 12:00PM - 1:00PM

Abstract: We consider obstacle problems for three nonlocal operators: 

A) The integral fractional Laplacian 

B) The integral fractional Laplacian with drift 

C) A second order elliptic operator plus the integral fractional Laplacian 
For the solution of the problem in Case A, we derive regularity results in weighted Sobolev spaces, where the weight is a power of the distance to the boundary. For cases B and C we derive, via a Lewy-Stampacchia type argument, regularity results in standard Sobolev spaces. We use these regularity results to derive error estimates for finite element schemes. The error estimates turn out to be optimal in Case A, whereas there is a loss of optimality in cases B and C, depending on the order of the integral operator.

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