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EnglishPh.D. Thesis Abstract A Boundary Value Problem for a PDE Model in Mass Transfer Theory: Representation of Solutions and Regularity Results. Elena Giorgieri Universit a 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 H older continuous function of exponent at least 2=3. We apply this result to the study of regularity of the solutions (in a suitable sense) of system (1) 8>>><>>>:
Giorgieri, E. (2006). A boundary value problem for a PDE model in mass transfer theory: representations of solutions and regularity results.
| Autori: | |
| Titolo: | A boundary value problem for a PDE model in mass transfer theory: representations of solutions and regularity results |
| Data di pubblicazione: | 23-feb-2006 |
| Anno Accademico: | 2004/2005 |
| Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
| Lingua: | en |
| Tipologia: | Tesi di dottorato |
| Citazione: | Giorgieri, E. (2006). A boundary value problem for a PDE model in mass transfer theory: representations of solutions and regularity results. |
| Appare nelle tipologie: | 07 - Tesi di dottorato |
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