Nonlinear degenerate elliptic partial differential equations with critical growth conditions on the gradient

Kwon Cho, Hi Jun Choe

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We consider a nonlinear degenerate elliptic partial differential equation with the critical growth condition on where g is sufficiently integrable and p is between 1 and ∞. Our first goal of this paper is to prove the existence of the solution.The main idea is to obtain the uniform L-estimate of suitable approximate solutions, employing a truncation technique and radially decreasing symmetrization techniques based on rearrangements. We also find an example of unbounded weak solution.

Original languageEnglish
Pages (from-to)3789-3796
Number of pages8
JournalProceedings of the American Mathematical Society
Issue number12
Publication statusPublished - 1995 Dec


All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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