IJPAM: Volume 51, No. 2 (2009)

Invited Lecture Delivered at
Fifth International Conference of Applied Mathematics
and Computing (Plovdiv, Bulgaria, August 12-18, 2008)


HARMONIC GRADIENTS, HÖLDER NORMS FOR ELLIPTIC
FUNCTIONS, AND SOLUTIONS TO POISSON'S
EQUATION ON A NONSMOOTH DOMAIN

Caroline Sweezy
Department of Mathematical Sciences
New Mexico State University
P.O. Box 30001, 3MB, Las Cruces
New Mexico, 88003-8001, USA
e-mail: [email protected]


Abstract.Solutions to $Lu=\text{\rm div}\,\overrightarrow{f}$ in a bounded, nonsmooth domain $\Omega $, $u=g$ on $\partial \Omega $, are investigated using a local Hölder norm of $u$ and different measures on $\Omega $. Results for 2-nd order strictly elliptic operators are presented, and problems that arise in proving similar theorems for their parabolic counterparts are discussed.

Received: August 14, 2008

AMS Subject Classification: 35J25, 35J15, 42B25

Key Words and Phrases: elliptic and parabolic equations, Lipschitz domains, Borel measures, Green functions, semi-discrete Littlewood-Paley type inequalities

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 51
Issue: 2