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http://hdl.handle.net/2108/211
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| 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 |
| Appears in Collections: | Tesi di dottorato in scienze matematiche e fisiche
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| tesi-07-12-04.pdf | | 708Kb | Adobe PDF | View/Open |
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