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4 votes

Symmetry Properties of Minimizers - Calculus of Variations

There are mainly two ways to get symmetry of minimizers, at least when the functional is associated to an elliptic PDE. The first one is the rearrangement argument (Schwarz symmetrization, Steiner sym …
Kelei Wang's user avatar
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Defining surface integral on boundary of $C^1$-domain

A general way to define this is to use rectifiable sets. For example, if $\Omega$ is a set of finite perimeter, measurable functions and their integrations are well defined. Moreover, the divergence t …
Kelei Wang's user avatar