Unique continuation of the quasilinear elliptic equation on lebesgue spaces Lp

R. E. Castillo, H. Rafeiro, E. M. Rojas

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

In this paper we make the convolution between φ, the fundamental solution of the Laplace equation, and function V that belongs to the space Ln/p (Rn). Since this convolution solves Poisson’s equation - Δz = V, we use this result to derive Fefferman’s inequality, which will be the cornerstone in the proof of our main result, which deals with the unique continuation property of the nonnegative solution of the quasilinear elliptic equation div A(x, u, ∇u) = B(x, u, ∇u), whose coefficients belong to the Ln/p (Rn) space.

Original languageEnglish
Pages (from-to)136-153
Number of pages18
JournalAzerbaijan Journal of Mathematics
Volume11
Issue number1
Publication statusPublished - Jan 2021

Keywords

  • Doubling condition
  • Fefferman’s inequality
  • Hedberg’s inequality
  • Unique continuation

ASJC Scopus subject areas

  • General Mathematics

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