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On the equivalence of viscosity and distribution solutions of second-order PDEs with Neumann boundary conditions |
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| Affiliation: | 1. School of Mathematics and Statistics, Jiangsu Normal University, 221116, Xuzhou, China;2. Fakultät für Mathematik, Universität Bielefeld, D-33501, Bielefeld, Germany;3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences (CAS), 100190, Beijing, China |
| Abstract: | We apply a probabilistic approach to prove that the viscosity solutions and the distribution ones to the Neumann problem of second order elliptic and parabolic equations are equivalent. |
| Keywords: | Neumann boundary condition Viscosity solution Distribution solution Comparison theorem |
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