Semilinear elliptic equations with Hardy potential and gradient nonlinearity

  • Konstantinos Gkikas

    National and Kapodistrian University of Athens, Greece
  • Phuoc-Tai Nguyen

    Masaryk University, Brno, Czechia
Semilinear elliptic equations with Hardy potential and gradient nonlinearity cover

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Abstract

Let () be a bounded domain, and let be the distance to . In this paper, we study positive solutions of the equation in , where , and is a continuous, nondecreasing function on . We prove that if satisfies a singular integral condition, then there exists a unique solution of with a prescribed boundary datum . When with , we show that equation~ admits a critical exponent (depending only on and ). In the subcritical case, namely , we establish some a priori estimates and provide a description of solutions with an isolated singularity on . In the supercritical case, i.e., , we demonstrate a removability result in terms of Bessel capacities.

Cite this article

Konstantinos Gkikas, Phuoc-Tai Nguyen, Semilinear elliptic equations with Hardy potential and gradient nonlinearity. Rev. Mat. Iberoam. 36 (2020), no. 4, pp. 1207–1256

DOI 10.4171/RMI/1164