Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



A sharp pointwise bound for functions with $ L\sp 2$-Laplacians on arbitrary domains and its applications

Author: Wenzheng Xie
Journal: Bull. Amer. Math. Soc. 26 (1992), 294-298
MSC (2000): Primary 26D15; Secondary 35Q53
MathSciNet review: 1126088
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For all functions on an arbitrary open set $ \Omega \subset {R^3}$ with zero boundary values, we prove the optimal bound

$\displaystyle \mathop {{\text{sup}}}\limits_\Omega \vert u\vert \leq {(2\pi )^{... ... }\vert\nabla u{\vert^2}dx{\smallint _\Omega }\vert\Delta u{\vert^2}dx)^{1/4}}.$

The method of proof is elementary and admits generalizations. The inequality is applied to establish an existence theorem for the Burgers equation.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 26D15, 35Q53

Retrieve articles in all journals with MSC (2000): 26D15, 35Q53

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society