Work

Existence of an extremal function of critical Sobolev embedding with an α -homogeneous weight

Year: 2025

Type: article

Abstract: In [ Calc. Var. Partial Differ. Equ. 60 (2021), no. 1, article no. 16 (27 pages)], we revisited a critical Sobolev-type embedding for weighted Sobolev spaces as introduced in [ J. Differ. Equations 255 (2013), no. 11, pp. 4312–4336] by Cabré and Ros-Oton. In the same paper, we announced to explore the existence of an extremal function within this framework. In this current work, we not only provide a positive affirmation to this inquiry but extend it to a broader range of weights known as α - homogeneous weights .

Source: Comptes Rendus Mathématique

DOI: 10.5802/crmath.718

Authors: Petr Gurka, Daniel Hauer

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Grantová Agentura České Republiky, Australian Research Council

Awards: Fine properties of functions, operators and function spaces, Optimal shapes in geometry and physics: Isoperimetry in modern analysis, G3298403960, Nonlinear harmonic analysis and dispersive partial differential equations

OpenAlex ID: W4410730389