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On Aleksandrov-Fenchel Inequalities for k-Convex Domains
On Aleksandrov-Fenchel Inequalities k-Convex Domains
2014/4/3
These are the lecture notes based on a course which the first named author has given at the second congress organized by the Riemann International School of Mathematics in Verbania, Italy from S...
$H^2$ regularity for the $p(x)-$Laplacian in two-dimensional convex domains
Variable exponent spaces Elliptic Equations H2 regularity
2011/9/9
Abstract: In this paper we study the $H^2$ global regularity for solutions of the $p(x)-$Laplacian in two dimensional convex domains with Dirichlet boundary conditions. Here $p:\Omega \to [p_1,\infty)...
We prove that a C1,1-smooth bounded domain D in Cn is linearly convex if and only if the convex hull of any two discs in D with common center lies in D.
Shape Optimization Problems over Classes of Convex Domains
Shape Optimization Problems Convex Domains
2009/2/5
We consider shape optimization problems of the form
\min\left\{\int_{\partial A} f(x,\nu(x))\hbox{d}x {\cal{H}^{n-1}} :A\in{\cal A}\right\}
where $f$ is any continuous function and the class ${\ca...