Some Properties of DeGiorgi Classes
Emmanuele DiBenedetto, Ugo Gianazza
TL;DR
This paper investigates properties of DeGiorgi classes, which include solutions to certain elliptic equations and variational minima, presenting new results, reviewing known facts, and discussing open problems.
Contribution
It introduces new properties of DeGiorgi classes and consolidates existing knowledge, highlighting open questions in the field.
Findings
New properties of DeGiorgi classes are established.
The paper reviews known facts about solutions and minima.
Open issues in the theory are formulated.
Abstract
The DeGiorgi classes , defined in (1.1) 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).
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