A boundary Harnack principle for equations with nonzero right hand side

Abstract: The boundary Harnack principle allows one to compare the behavior of two harmonic solutions when they both vanish on the boundary. This principle has proven useful in PDE, harmonic analysis, and free boundary problems. In this talk I will review the principle and some of its applications. I will then introduce a new boundary Harnack principle for functions whose Laplacian has nonzero right hand sides. This new principle has applications to Hele-Shaw flow as well as free boundary problems. I will also show how we have recently proven this result for fully nonlinear equations as well as the p-Laplacian. This is joint work with Dennis Kriventsov and Henrik Shahgholian.

analysis of PDEs

Audience: researchers in the topic

Rio de Janeiro webinar on analysis and partial differential equations

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