Doubling inequalities for nonlinear elliptic PDEs

Abstract: Fully nonlinear elliptic PDEs include the Monge-Ampere equation from optimal transport and the PDEs for constructing minimal surfaces of high codimension. Such PDEs can be solved in the weak, viscosity sense, so the question is whether such solutions are smooth, or what kinds of singularities are possible. In the past, these questions were solved for each equation using very different approaches. In this talk, we indicate a unified approach to these questions and equations, based on the idea of a doubling inequality.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

OARS Online Analysis Research Seminar

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