Work

Boundary Behavior of Positive Solutions of Semilinear Elliptic Equations with Negative Exponent

Year: 2026

Type: article

Abstract: We estimate the Hausdorff dimension of a subset of the unit sphere where a positive solution of a semilinear elliptic equation with source term of negative exponent in the unit ball grows faster than a prescribed order. Also, the sharpness of our estimate is shown by proving the existence of a positive solution growing faster than a prescribed order on a given subset of the unit sphere.

Source: Mediterranean Journal of Mathematics

DOI: 10.1007/s00009-026-03180-6

Author: Kentaro Hirata

Institution: Hiroshima University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Japan Society for the Promotion of Science