An application of approximation to comparison principles for viscosity solutions of curvature equations
β Scribed by Y. Luo; A. Eberhard
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 214 KB
- Volume
- 64
- Category
- Article
- ISSN
- 0362-546X
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π SIMILAR VOLUMES
We establish two comparison results, between the solutions of a class of mean curvature equations and pieces of arcs of circles that satisfy the same Neumann boundary condition. Finally we present a number of examples where our estimates can be applied; some of them have a physical motivation.
Let be either a ball or an annulus centered about the origin in N and p the usual p-Laplace operator in Ξ² β 0 1 be any two radial weak solutions ofp u i = b u i + f i in . We then show that u 1 β€ u 2 in implies u 1 < u 2 in and also that appropriate versions of Hopf boundary point principle hold.