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Transactions of the American Mathematical Society

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

 

 

Liouville theorems, partial regularity and Hölder continuity of weak solutions to quasilinear elliptic systems


Author: Michael Meier
Journal: Trans. Amer. Math. Soc. 284 (1984), 371-387
MSC: Primary 35B65; Secondary 35D10, 35J60
MathSciNet review: 742430
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Abstract: This paper describes the connections between Liouville type theorems and interior regularity results for bounded weak solutions of quasilinear elliptic systems with quadratic growth. It is shown that equivalence does in general hold only in some restricted sense. A complete correspondence can be established in certain cases, e.g. for small solutions and for minima of quadratic variational integrals.


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DOI: https://doi.org/10.1090/S0002-9947-1984-0742430-X
Keywords: Quasilinear elliptic systems, weak solutions, regularity, Liouville theorems, reverse Hölder inequality
Article copyright: © Copyright 1984 American Mathematical Society