Continuous dependence results for Non-linear Neumann type boundary value problems

Details Continuous dependence results for Non-linear Neumann type boundary value problems Continuous dependence results for Non-linear Neumann type boundary value problems

2008-07-10

arxiv.org/abs/0807.1633v1

Mathematics

Analysis of PDEs

Scientific paper

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-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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