Work

Unique Continuation from Conical Boundary Points for Fractional Equations

Year: 2025

Type: article

Abstract: . We provide fine asymptotics of solutions of fractional elliptic equations at boundary points where the domain is locally conical; that is, corner type singularities appear. Our method relies on a suitable smoothing of the corner singularity and an approximation scheme, which allow us to provide a Pohozaev- type inequality. Then the asymptotics of solutions at the conical point follow by an Almgren-type monotonicity formula, blow-up analysis, and Fourier decomposition on eigenspaces of a spherical eigenvalue problem. A strong unique continuation principle follows as a corollary.

Source: SIAM Journal on Mathematical Analysis

DOI: 10.1137/24m1663193

Authors: Alessandra De Luca, Veronica Felli, Stefano Vita

Institutions: University of Turin, University of Milano-Bicocca, University of Pavia

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni, NextGenerationEU