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Please use this identifier to cite or link to this item: http://hdl.handle.net/2108/211

Title: A boundary value problem for a PDE model in mass transfer theory: representations of solutions and regularity results
Authors: Cannarsa, Piermarco
Giorgieri, Elena
Keywords: granular matter
eikonal equation
singularities
semiconcave functions
Issue Date: 23-Feb-2006
Abstract: Ph.D. Thesis Abstract A Boundary Value Problem for a PDE Model in Mass Transfer Theory: Representation of Solutions and Regularity Results. Elena Giorgieri Universita di Roma Tor Vergata Roma, Italia, e-mail: giorgier@mat.uniroma2.it Given a bounded domain  IRn, let us denote by d() : ! IR the distance function from the boundary @ . The set of points x 2 at which d is not di erentiable is called the singular set of d and denoted by . Its closure is often referred to as the cut locus. We introduce the map  : ! IR, de ned by  (x) = ( min nt  0 : x + tDd(x) 2 o x 2 n 0 x 2 ; which is sometimes called the maximal retraction length of onto  or normal distance to . The aim of this work is two{sided: 1 To present a global regularity result on the normal distance to the cut locus, showing that in the case when n = 2 and is a bounded simply connected domain with analytic boundary, then  is either a Lipschitz continuous or a Holder continuous ...
URI: http://hdl.handle.net/2108/211
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