21,577 research outputs found
A Bernoulli problem with non constant gradient boundary constraint
We present in this paper a result about existence and convexity of solutions
to a free boundary problem of Bernoulli type, with non constant gradient
boundary constraint depending on the outer unit normal. In particular we prove
that, in the convex case, the existence of a subsolution guarantees the
existence of a classical solution, which is proved to be convex.Comment: 8 pages, no figure
A note on an overdetermined problem for the capacitary potential
We consider an overdetermined problem arising in potential theory for the
capacitary potential and we prove a radial symmetry result.Comment: 7 pages. This paper has been written for possible publication in a
special volume dedicated to the conference "Geometric Properties for
Parabolic and Elliptic PDE's. 4th Italian-Japanese Workshop", organized in
Palinuro in May 201
Wulff shape characterizations in overdetermined anisotropic elliptic problems
We study some overdetermined problems for possibly anisotropic degenerate
elliptic PDEs, including the well-known Serrin's overdetermined problem, and we
prove the corresponding Wulff shape characterizations by using some integral
identities and just one pointwise inequality. Our techniques provide a somehow
unified approach to this variety of problems
Soft congestion approximation to the one-dimensional constrained Euler equations
This article is concerned with the analysis of the one-dimensional
compressible Euler equations with a singular pressure law, the so-called hard
sphere equation of state. The result is twofold. First, we establish the
existence of bounded weak solutions by means of a viscous regularization and
refined compensated compactness arguments. Second, we investigate the smooth
setting by providing a detailed description of the impact of the singular
pressure on the breakdown of the solutions. In this smooth framework, we
rigorously justify the singular limit towards the free-congested Euler
equations, where the compressible (free) dynamics is coupled with the
incompressible one in the constrained (i.e. congested) domain
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