Nodal sets of solutions of elliptic and parabolic equations
โ Scribed by Fang-Hua Lin
- Publisher
- John Wiley and Sons
- Year
- 1991
- Tongue
- English
- Weight
- 772 KB
- Volume
- 44
- Category
- Article
- ISSN
- 0010-3640
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๐ SIMILAR VOLUMES
In this paper, we develop a Sturm Liouville type theory for the nodal sets and Morse indices of solutions of super-linear elliptic PDEs with Dirichlet boundary condition. It shows that there are some relationships between analytic properties (e.g., L p -norm, vanishing order of the nodal point, and
The elliptic equation \(\Delta u+f(u)=0\) in \(R^{n}\) is discussed in the case where \(f(u)=\) \(|u|^{n} \quad u(|u| \geqslant 1),=|u|^{4} \quad{ }^{1} u(|u|<1), 10\). It is further proved that for any \(k \geqslant 0\) there exist at least three radially symmetric solutions which have exactly \(k\
## Abstract We introduce a measure for the starshapedness of the level sets of solutions of certain nonlinear elliptic equations in a starshaped ring ฮฉ of IR^n^. We prove that a function which characterizes the starshapedness does not attain its minimum in ฮฉ.
Various classes of non-uniformly elliptic (and parabolic) equations of second order of the form for all solutions u ( x ) of which m a n Iuzl can be estimated by maxn [uI and m a a R JuxJ, were discussed in [I] (see also [2]).l The method used was introduced in [3]. In the same paper a method was s