On the nodal set of solutions to degenerate or singular elliptic equations with an application to $s-$harmonic functions
| Autor: | Giorgio Tortone, Susanna Terracini, Yannick Sire |
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| Rok vydání: | 2018 |
| Předmět: |
Nodal set
Pure mathematics Class (set theory) Applied Mathematics General Mathematics Nonlocal diffusion 010102 general mathematics Degenerate energy levels Extension (predicate logic) Blow-up classification Degenerate or singular elliptic equations Monotonicity formulas 01 natural sciences Stratification (mathematics) 010101 applied mathematics Mathematics - Analysis of PDEs Harmonic function Dimension (vector space) FOS: Mathematics Complete theory 0101 mathematics Link (knot theory) Mathematics Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.1808.01851 |
| Popis: | This work is devoted to the geometric-theoretic analysis of the nodal set of solutions to degenerate or singular equations involving a class of operators including L a = div ( | y | a ∇ ) , with a ∈ ( − 1 , 1 ) and their perturbations. As they belong to the Muckenhoupt class A 2 , these operators appear in the seminal works of Fabes, Kenig, Jerison and Serapioni [1] , [2] , [3] and have recently attracted a lot of attention in the last decade due to their link to the localization of the fractional Laplacian via the extension in one more dimension [4] . Our goal in the present paper is to develop a complete theory of the stratification properties for the nodal set of solutions of such equations in the spirit of the seminal works of Hardt, Simon, Han and Lin [5] , [6] , [7] . |
| Databáze: | OpenAIRE |
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