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FRB

Seminar

A classical Perron method for existence of smooth solutions to boundary value & obstacle problems for boundary-degenerate elliptic operators via holomorphic map

Feehan, P (Rutgers, The State University of New Jersey)
Thursday 19 June 2014, 14:00-15:00

Seminar Room 1, Newton Institute

Abstract

We prove existence of solutions to boundary value problems and obstacle problems for degenerate-elliptic, linear, second-order partial differential operators with partial Dirichlet boundary conditions using a new version of the Perron method. The elliptic operators considered have a degeneracy along a portion of the domain boundary which is similar to the degeneracy of a model linear operator identified by Daskalopoulos and Hamilton (1998) in their study of the porous medium equation or the degeneracy of the Heston operator (Heston, 1993) in mathematical finance. Our Perron method relies on weak and strong maximum principles for degenerate-elliptic operators, concepts of continuous subsolutions and supersolutions for boundary value and obstacle problems for degenerate-elliptic operators, and maximum and comparison principle estimates previously developed by us.

Presentation

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