Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids
Sobolev regularity via the convergence rate of convolutions and Jensen’s inequality
We derive a new criterion for a real-valued function to be in the Sobolev space . This criterion consists of comparing the value of a functional with the values of the same functional applied to convolutions of with a Dirac sequence. The difference of these values converges to zero as the convolutions approach , and we prove that the rate of convergence to zero is connected to regularity: if and only if the convergence is sufficiently fast. We finally apply our criterium to a minimization...
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