Work

Sharp radial Sobolev inequalities with inverse square potentials and applications to nonlinear Schrödinger equations

Year: 2026

Type: article

Abstract: We prove the sharp radial Sobolev inequality with a repulsive inverse square potential. Considered all $\dot{H}^{1} $ functions, the inequality is not attained by non-trivial function. In this paper, we show that the inequality is attained under radial restriction. As its application, we put on global dynamics of solutions to nonlinear Schrödinger equation with the potential, whose energy is less than or equal to that of the optimizer to the inequality.

Source: Journal of Inequalities and Applications

DOI: 10.1186/s13660-026-03479-8

Authors: Masaru Hamano, Masahiro Ikeda

Institutions: Kyoto University, The University of Osaka

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,190

Funders: Japan Society for the Promotion of Science, Core Research for Evolutional Science and Technology