publication . Preprint . 2013

Maximum principles for boundary-degenerate linear parabolic differential operators

Feehan, Paul M. N.;
Open Access English
  • Published: 20 Jun 2013
We develop weak and strong maximum principles for boundary-degenerate, linear, parabolic, second-order partial differential operators, $Lu := -u_t-\tr(aD^2u)-\langle b, Du\rangle + cu$, with \emph{partial} Dirichlet boundary conditions. The coefficient, $a(t,x)$, is assumed to vanish along a non-empty open subset, $\mydirac_0!\sQ$, called the \emph{degenerate boundary portion}, of the parabolic boundary, $\mydirac!\sQ$, of the domain $\sQ\subset\RR^{d+1}$, while $a(t,x)$ may be non-zero at points in the \emph{non-degenerate boundary portion}, $\mydirac_1!\sQ := \mydirac!\sQ\less\bar{\mydirac_0!\sQ}$. Points in $\mydirac_0!\sQ$ play the same role as those in the ...
free text keywords: Mathematics - Analysis of PDEs, Mathematics - Probability, Primary 35B50, 35B51, 35K65, secondary 35D40, 35K85, 60J60
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Funded by
NSF| AMC-SS: Mathematical Finance and Partial Differential Equations Conference - November 2, 2012
  • Funder: National Science Foundation (NSF)
  • Project Code: 1237722
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
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