Abstract
We prove comparison results between continuous and discontinuous viscosity sub- and super-solutions of the generalized Dirichlet problem for quasilinear elliptic and parabolic equations. The main consequence of these results is the uniqueness of continuous solutions of such problems, when they exist.
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Barles, G., Rouy, E., Souganidis, P.E. (1999). Remarks on the Dirichlet Problem for Quasilinear Elliptic and Parabolic Equations. In: McEneaney, W.M., Yin, G.G., Zhang, Q. (eds) Stochastic Analysis, Control, Optimization and Applications. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1784-8_12
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DOI: https://doi.org/10.1007/978-1-4612-1784-8_12
Publisher Name: Birkhäuser, Boston, MA
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