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.
Mots-clés : Unique continuation, Singular weights, Conical geometry, Blow-up limits, Almgren's frequency formula
@article{AIHPC_2020__37_4_785_0,
author = {Dipierro, Serena and Felli, Veronica and Valdinoci, Enrico},
title = {Unique continuation principles in cones under nonzero {Neumann} boundary conditions},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {785--815},
publisher = {Elsevier},
volume = {37},
number = {4},
year = {2020},
doi = {10.1016/j.anihpc.2020.01.005},
mrnumber = {4104826},
zbl = {1479.35287},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2020.01.005/}
}
TY - JOUR AU - Dipierro, Serena AU - Felli, Veronica AU - Valdinoci, Enrico TI - Unique continuation principles in cones under nonzero Neumann boundary conditions JO - Annales de l'I.H.P. Analyse non linéaire PY - 2020 SP - 785 EP - 815 VL - 37 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2020.01.005/ DO - 10.1016/j.anihpc.2020.01.005 LA - en ID - AIHPC_2020__37_4_785_0 ER -
%0 Journal Article %A Dipierro, Serena %A Felli, Veronica %A Valdinoci, Enrico %T Unique continuation principles in cones under nonzero Neumann boundary conditions %J Annales de l'I.H.P. Analyse non linéaire %D 2020 %P 785-815 %V 37 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2020.01.005/ %R 10.1016/j.anihpc.2020.01.005 %G en %F AIHPC_2020__37_4_785_0
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. http://archive.numdam.org/articles/10.1016/j.anihpc.2020.01.005/
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