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Some Properties of DeGiorgi Classes

Published 2016-04-26Version 1

The DeGiorgi classes $[DG]_p(E;\gamma)$, defined in (1.1)${}_{\pm}$ below encompass, solutions of quasilinear elliptic equations with measurable coefficients as well as minima and Q-minima of variational integrals. For these classes we present some new results (\S 2 and \S 3.1), and some known facts scattered in the literature (\S 3-\S 5), and formulate some open issues (\S 6).

Categories: math.AP

Subjects: 35J15, 49N60, 35J92

Keywords: degiorgi classes, properties, quasilinear elliptic equations, variational integrals, open issues

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