Continuous dependence results for non-linear Neumann type boundary value problems |
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Authors: | Espen R Jakobsen Christine A Georgelin |
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Institution: | a Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway b Laboratoire de Mathématiques et Physique Théorique, Faculté des Sciences et Techniques, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, 37200 Tours, France |
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Abstract: | We obtain estimates on the continuous dependence on the coefficient for second-order non-linear degenerate Neumann type boundary value problems. Our results extend previous work of Cockburn et al., Jakobsen and Karlsen, and Gripenberg to problems with more general boundary conditions and domains. A new feature here is that we account for the dependence on the boundary conditions. As one application of our continuous dependence results, we derive for the first time the rate of convergence for the vanishing viscosity method for such problems. We also derive new explicit continuous dependence on the coefficients results for problems involving Bellman-Isaacs equations and certain quasilinear equation. |
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Keywords: | 35J25 35J60 35J70 49L25 |
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