Proceedings of the American Mathematical Society

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A remark on Bony maximum principle


Author: P.-L. Lions
Journal: Proc. Amer. Math. Soc. 88 (1983), 503-508
MSC: Primary 35J65; Secondary 35B50
MathSciNet review: 699422
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Abstract: We extend a result due to J. M. Bony concerning a form of the classical maximum principle adapted to Sobolev spaces. We treat the case of the limiting exponent and show that the result is optimal. We give various applications to nonlinear elliptic partial differential equations.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0699422-3
Keywords: Sobolev spaces, maximum principle, second-order elliptic equations, viscosity solutions
Article copyright: © Copyright 1983 American Mathematical Society