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1 April 2005 Conservation laws for equations of mixed elliptic-hyperbolic and degenerate types
Daniela Lupo, Kevin R. Payne
Duke Math. J. 127(2): 251-290 (1 April 2005). DOI: 10.1215/S0012-7094-04-12722-8

Abstract

For partial differential equations of mixed elliptic-hyperbolic and degenerate types which are the Euler-Lagrange equations for an associated Lagrangian, invariance with respect to changes in independent and dependent variables is investigated, as are results in the classification of continuous one-parameter symmetry groups. For the variational and divergence symmetries, conservation laws are derived via the method of multipliers. The conservation laws resulting from anisotropic dilations are applied to prove uniqueness theorems for linear and nonlinear problems, and the invariance under dilations of the linear part is used to derive critical exponent phenomena and to obtain localized energy estimates for supercritical problems.

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Daniela Lupo. Kevin R. Payne. "Conservation laws for equations of mixed elliptic-hyperbolic and degenerate types." Duke Math. J. 127 (2) 251 - 290, 1 April 2005. https://doi.org/10.1215/S0012-7094-04-12722-8

Information

Published: 1 April 2005
First available in Project Euclid: 23 March 2005

zbMATH: 1078.35078
MathSciNet: MR2130413
Digital Object Identifier: 10.1215/S0012-7094-04-12722-8

Subjects:
Primary: 35L65 , 35M10 , 58J70
Secondary: 35A05 , 35B33

Rights: Copyright © 2005 Duke University Press

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Vol.127 • No. 2 • 1 April 2005
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