The strong maximum principle is proved to hold for weak (in the sense of support functions) sub-and supersolutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for C 0 -space-like hypersurfaces in a Lorentzian manifold. As one application, a Lorentzian warp
Strong Comparison Principle for Radial Solutions of Quasi-Linear Equations
โ Scribed by S Prashanth
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 75 KB
- Volume
- 258
- Category
- Article
- ISSN
- 0022-247X
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โฆ Synopsis
Let be either a ball or an annulus centered about the origin in N and p the usual p-Laplace operator in
ฮฒ โ 0 1 be any two radial weak solutions ofp u i = b u i + f i in . We then show that u 1 โค u 2 in implies u 1 < u 2 in and also that appropriate versions of Hopf boundary point principle hold.
๐ SIMILAR VOLUMES
We present a quasi maximum principle stating roughly that holomorphic solutions of a given partial differential equation with constant coefficents in C n , achieve essentially their maximal growth on a certain algebraic hypersurface 1 related to the operator. We prove it in the case where P is homo
In this paper we consider the nonlinear third-order quasi-linear differential equation and obtain some simple conditions for the existence of a periodic solution for it. In so doing we use the implicit function theorem to prove a theorem about the existence of periodic solutions and consider one ex