통합자연과학논문집 (Journal of Integrative Natural Science)

조선대학교 기초과학연구원 (The Basic Science Institute Chosun University)
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A Priori Boundary Estimations for an Elliptic Operator

  • Cho, Sungwon (Department of Mathematics Education, Gwangju National University of Education)
  • 투고 : 2014.12.07
  • 심사 : 2014.12.25
  • 발행 : 2014.12.31
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초록

In this article, we consider a singular and a degenerate elliptic operators in a divergence form. The singularities exist on a part of boundary, and comparable to the logarithmic distance function or its inverse. If we assume that the operator can be treated in a pointwise sense than distribution sense, with this operator we obtain a priori Harnack continuity near the boundary. In the proof we transform the singular elliptic operator to uniformly bounded elliptic operator with unbounded first order terms. We study this type of estimations considering a De Giorgi conjecture. In his conjecture, he proposed a certain ellipticity condition to guarantee a continuity of a solution.

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참고문헌

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