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Harnack's inequality for a nonlinear eigenvalue problem on metric spaces |
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| Authors: | Visa Latvala Mikko Pere |
| Affiliation: | a Department of Mathematics, University of Joensuu, PO Box 111 FI-80101 Joensuu, Finland b Institute of Mathematics, Helsinki University of Technology, PO Box 1100 FI-02015, Finland c Department of Mathematics and Statistics, University of Helsinki, PO Box 68 FI-00014, Finland |
| Abstract: | We prove Harnack's inequality for first eigenfunctions of the p-Laplacian in metric measure spaces. The proof is based on the famous Moser iteration method, which has the advantage that it only requires a weak (1,p)-Poincaré inequality. As a by-product we obtain the continuity and the fact that first eigenfunctions do not change signs in bounded domains. |
| Keywords: | Caccioppoli estimate Doubling measure First eigenvalue First eigenfunction Harnack's inequality Metric space Minimizer Newtonian space Nonlinear eigenvalue problem Poincaré inequality Rayleigh quotient Superminimizer Sobolev space |
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