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http://dx.doi.org/10.14403/jcms.2014.27.4.763

A CERTAIN EXAMPLE FOR A DE GIORGI CONJECTURE

Cho, Sungwon (Department of Mathematics Education Gwangju National University of Education)

Publication Information

Journal of the Chungcheong Mathematical Society / v.27, no.4, 2014 , pp. 763-769 More about this Journal

Abstract

In this paper, we illustrate a counter example for the converse of a certain conjecture proposed by De Giorgi. De Giorgi suggested a series of conjectures, in which a certain integral condition for singularity or degeneracy of an elliptic operator is satisfied, the solutions are continuous. We construct some singular elliptic operators and solutions such that the integral condition does not hold, but the solutions are continuous.

Keywords

singular elliptic partial differential equation; Degenerate elliptic partial differential equation; Continuity of a weak solution;

Citations & Related Records

Reference

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