On the Asymptotic Dirichlet Problem for the Minimal Hypersurface Equation in a Hadamard Manifold
| Autor: | Jaime Ripoll, Ilkka Holopainen, Jean-Baptiste Casteras |
|---|---|
| Přispěvatelé: | Quantitative methods for stochastic models in physics (MEPHYSTO), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université libre de Bruxelles (ULB), Département de mathématiques Université Libre de Bruxelles, Université libre de Bruxelles (ULB), Helsingin yliopisto = Helsingfors universitet = University of Helsinki, Instituto de Matematica [Porto Alegre, RS] (IM/UFRGS), Universidade Federal do Rio Grande do Sul [Porto Alegre] (UFRGS), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, University of Helsinki, Department of Mathematics and Statistics, Instituto de Matematica ( Universidade Federal do Rio Grande do Sul) |
| Rok vydání: | 2017 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Invariant manifold Minimal graph equation 01 natural sciences symbols.namesake 58J32 53C21 31C45 Dirichlet eigenvalue Dirichlet's principle 111 Mathematics FOS: Mathematics INFINITY NONSOLVABILITY Hadamard manifold DIFFEOMORPHISMS 0101 mathematics Nehari manifold ComputingMilieux_MISCELLANEOUS Dirichlet problem Mathematics SURFACES 010102 general mathematics Mathematical analysis ELLIPTIC-OPERATORS Dirichlet's energy Mathematics::Spectral Theory NEGATIVELY CURVED MANIFOLDS 010101 applied mathematics KILLING GRAPHS MEAN-CURVATURE Differential Geometry (math.DG) [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] M X R Dirichlet boundary condition symbols Mathematics::Differential Geometry Analysis HARMONIC-FUNCTIONS |
| Zdroj: | Potential Analysis Potential Analysis, 2017, 47 (4), pp.485-501. ⟨10.1007/s11118-017-9624-z⟩ Potential Analysis, Springer Verlag, 2017, 47 (4), pp.485-501. ⟨10.1007/s11118-017-9624-z⟩ |
| ISSN: | 1572-929X 0926-2601 |
| DOI: | 10.1007/s11118-017-9624-z |
| Popis: | We study the Dirichlet problem at infinity on a Cartan-Hadamard manifold M of dimension n 2 for a large class of operators containing, in particular, the p-Laplacian and the minimal graph operator. We extend several existence results obtained for the p-Laplacian to our class of operators. As an application of our main result, we prove the solvability of the asymptotic Dirichlet problem for the minimal graph equation for any continuous boundary data on a (possibly non rotationally symmetric) manifold whose sectional curvatures are allowed to decay to 0 quadratically. |
| Databáze: | OpenAIRE |
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