Geodesic
Unique continuation principles in cones under nonzero Neumann boundary conditions
Dipierro, Serena1 ; Felli, Veronica2 ; Valdinoci, Enrico1
1 Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia
2 Dipartimento di Scienza dei Materiali, Università di Milano-Bicocca, Via Cozzi 55, 20125 Milano, Italy
Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 4, pp. 785-815

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We consider an elliptic equation in a cone, endowed with (possibly inhomogeneous) Neumann conditions. The operator and the forcing terms can also allow non-Lipschitz singularities at the vertex of the cone.

In this setting, we provide unique continuation results, both in terms of interior and boundary points.

The proof relies on a suitable Almgren-type frequency formula with remainders. As a byproduct, we obtain classification results for blow-up limits.

DOI : 10.1016/j.anihpc.2020.01.005
Classification : 35J15, 35J25, 35J75
Keywords: Unique continuation, Singular weights, Conical geometry, Blow-up limits, Almgren's frequency formula

Dipierro, Serena 1 ; Felli, Veronica 2 ; Valdinoci, Enrico 1

1 Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia
2 Dipartimento di Scienza dei Materiali, Università di Milano-Bicocca, Via Cozzi 55, 20125 Milano, Italy 
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     title = {Unique continuation principles in cones under nonzero {Neumann} boundary conditions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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Dipierro, Serena; Felli, Veronica; Valdinoci, Enrico. Unique continuation principles in cones under nonzero Neumann boundary conditions. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 4, pp. 785-815. doi: 10.1016/j.anihpc.2020.01.005

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