Work

On a fractional boundary version of Talenti’s inequality in the unit ball

Year: 2025

Type: article

Abstract: Inspired by recent work of Ferone and Volzone (2021), we derive sufficient conditions for the validity and non-validity of a boundary version of Talenti’s comparison principle in the context of Dirichlet–Poisson problems for the fractional Laplacian ( − Δ ) s in the unit ball Ω = B 1 ( 0 ) ⊂ R N , s ∈ ( 0 , 1 ) . In particular, our results imply a universal failure of the classical pointwise Talenti inequality in the fractional radial context. In contrast, a boundary Talenti type inequality holds for radial functions in the higher order case s > 1 .

Source: Nonlinear Analysis Real World Applications

DOI: 10.1016/j.nonrwa.2025.104482

Authors: Yassin El Karrouchi, Tobias Weth

Institution: Goethe University Frankfurt

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,780

OpenAlex ID: W4413924660

FWCI:

Cites: 12

Cited by:

Related to: 10