IJPAM: Volume 42, No. 2 (2008)

WEIGHTED NORM BOUNDS FOR A LOCAL HÖLDER
NORM OF ELLIPTIC AND OF PARABOLIC FUNCTIONS
ON A NON-SMOOTH DOMAIN IN EUCLIDEAN SPACE

Caroline Sweezy
Department of Mathematical Sciences
College of Arts and Sciences
New Mexico State University
P.O. Box 30001, MSC 3MB, Las Cruces, New Mexico, 88003-8001, USA
e-mail: csweezy@nmsu.edu


Abstract.The rate of change of $u$, a solution to $Lu=\text{\rm div}
\overrightarrow{f}$ in a bounded, nonsmooth domain $\Omega $, $u=0$ on $%
\partial \Omega $, is investigated using a local Hölder norm of $u$ and different measures on $\Omega $. Results for both $L=\sum\limits_{i,j=1}^{d}%
\frac{\partial }{\partial x_{i}}(a_{i,j}(x)\frac{\partial }{\partial x_{j}})$ and for $L=\partial /\partial t-\sum\limits_{i,j=1}^{d}\frac{\partial }{%
\partial x_{i}}(a_{i,j}(x,t)\frac{\partial }{\partial x_{j}})$ are presented.

Received: August 17, 2007

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: 2008
Volume: 42
Issue: 2