In this paper, we prove the Pohozaev identity for the following fractional nonlinear elliptic equation: (Formula presented.) where N≥2, s∈(0,1), (-Δ)s denotes the fractional Laplacian operator, and g:R→R is a locally Hölder continuous function. Our proof rests on a regularity result for bounded distributional solutions of the above equation, an integration by parts formula for Ds,2∩C2s+ε functions with locally bounded gradient and vector fields of class Cc0,1, and a limiting procedure.
The Fractional Pohozaev identity in RN / Ambrosio, V.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 35:(2025). [10.1007/s12220-025-02083-4]
The Fractional Pohozaev identity in RN
Ambrosio V.
2025-01-01
Abstract
In this paper, we prove the Pohozaev identity for the following fractional nonlinear elliptic equation: (Formula presented.) where N≥2, s∈(0,1), (-Δ)s denotes the fractional Laplacian operator, and g:R→R is a locally Hölder continuous function. Our proof rests on a regularity result for bounded distributional solutions of the above equation, an integration by parts formula for Ds,2∩C2s+ε functions with locally bounded gradient and vector fields of class Cc0,1, and a limiting procedure.| File | Dimensione | Formato | |
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FRACPOHW-JGEANV.pdf
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