Characterization of Fractional Sobolev–Poincaré and (Localized) Hardy Inequalities

We prove that positive solutions of the fractional Lane–Emden equation with homogeneous Dirichlet boundary conditions satisfy pointwise estimates in terms of the best constant in Poincaré’s inequality on all open sets, and are isolated in $$L^1$$ L 1 on smooth bounded ones, whence we deduce the isolation of the first non-local semilinear eigenvalue.

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On Morrey's inequality in Sobolev-Slobodeckiĭ spaces

Brasco,

Prinari,

2024

Journal of Functional Analysis

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Characterization of Fractional Sobolev–Poincaré and (Localized) Hardy Inequalities

Cited by 4 publications

References 31 publications

On the sharp Hardy inequality in Sobolev–Slobodeckiĭ spaces

On the sharp Hardy inequality in Sobolev–Slobodeckiĭ spaces

A non-local semilinear eigenvalue problem

On Morrey's inequality in Sobolev-Slobodeckiĭ spaces

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