JournalsaihpcVol. 37, No. 4pp. 785–815

Unique continuation principles in cones under nonzero Neumann boundary conditions

  • Serena Dipierro

    Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia

  • Veronica Felli

    Dipartimento di Scienza dei Materiali, Università di Milano-Bicocca, Via Cozzi 55, 20125 Milano, Italy

  • Enrico Valdinoci

    Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia
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Abstract

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.

Cite this article

Serena Dipierro, Veronica Felli, Enrico Valdinoci, Unique continuation principles in cones under nonzero Neumann boundary conditions. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 4, pp. 785–815

DOI 10.1016/J.ANIHPC.2020.01.005