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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Local vanishing properties of solutions of elliptic and parabolic quasilinear equations


Authors: J. Ildefonso Díaz and Laurent Véron
Journal: Trans. Amer. Math. Soc. 290 (1985), 787-814
MSC: Primary 35B05; Secondary 35J60, 35K55
DOI: https://doi.org/10.1090/S0002-9947-1985-0792828-X
MathSciNet review: 792828
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Abstract: We use a local energy method to study the vanishing property of the weak solutions of the elliptic equation $ - \operatorname{div}\;A(x,u,Du) + B(x,u,Du) = 0$ and of the parabolic equation $ \partial \psi (u)/\partial t - \operatorname{div}\;\mathcal{A}(t,x,u,Du) + \mathcal{B}(t,x,u,Du) = 0$. The results are obtained without any assumption of monotonicity on $ A$, $ B$, $ \mathcal{A}$ and $ \mathcal{B}$.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0792828-X
Keywords: Elliptic equations, parabolic equations, weak solutions, local energy estimates, differential inequalities, trace-interpolation estimates, free boundary, propagation phenomena
Article copyright: © Copyright 1985 American Mathematical Society