Publication details

Semilinear elliptic equations with Hardy potential and gradient nonlinearity


GKIKAS Konstantinos NGUYEN Phuoc Tai

Year of publication 2020
Type Article in Periodical
Magazine / Source Revista Matematica Iberoamericana
MU Faculty or unit

Faculty of Science

Keywords Hardy potential; Martin kernel; boundary trace; critical exponent; gradient term; isolated singularities; removable singularities
Description Let Omega subset of R-N (N >= 3) be a C-2 bounded domain, and let delta be the distance to partial derivative Omega. In this paper, we study positive solutions of the equation ((*)) - L(mu)u + g(vertical bar del u vertical bar) = 0 in Omega), where L-mu = Delta + mu/delta(2), mu is an element of (0, 1/4] and g is a continuous, nondecreasing function on R+. We prove that if g satisfies a singular integral condition, then there exists a unique solution of ((*)) with a prescribed boundary datum v. When g(t) = t(q) with q is an element of (1, 2), we show that equation ((*)) admits a critical exponent q(mu) (depending only on N and mu). In the subcritical case, namely 1 < q < q(mu), we establish some a priori estimates and provide a description of solutions with an isolated singularity on partial derivative Omega. In the supercritical case, i.e., q(mu) <= q < 2, we demonstrate a removability result in terms of Bessel capacities.
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