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Transactions of the American Mathematical Society

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


Author: William Bertiger
Journal: Trans. Amer. Math. Soc. 238 (1978), 213-227
MSC: Primary 35B45; Secondary 35D99, 35J15
DOI: https://doi.org/10.1090/S0002-9947-1978-0482916-6
MathSciNet review: 482916
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Abstract: Weak solutions to second order elliptic equations and the first derivatives of these solutions are shown to satisfy $ {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.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0482916-6
Article copyright: © Copyright 1978 American Mathematical Society

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