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

Meier, Michael

doi:10.1090/S0002-9947-1984-0742430-X

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

Trans. Amer. Math. Soc. 284 (1984), 371-387

DOI: https://doi.org/10.1090/S0002-9947-1984-0742430-X

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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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