Maximum principles, gradient estimates, and weak solutions for second-order partial differential equations

Weak solutions to second order elliptic equations and the first derivatives of these solutions are shown to satisfy Lp{L^p} bounds. Classical second order equations with nonnegative characteristic form are also considered. It is proved that auxiliary functions of the gradient of a solution must sati...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 1978-01, Vol.238, p.213-227
Main Author: Bertiger, William
Format: Article
Language:English
Subjects:
Coefficients
Elliptic equations
Higher order derivatives
Integers
Mathematical functions
Mathematical theorems
Matrices
Maximum principle
Partial differential equations
Research article
Trajectories
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Summary:Weak solutions to second order elliptic equations and the first derivatives of these solutions are shown to satisfy Lp{L^p} bounds. Classical second order equations with nonnegative characteristic form are also considered. It is proved that auxiliary functions of the gradient of a solution must satisfy a maximum principle. This result is extended to higher order derivatives and systems.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-1978-0482916-6