๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Nodal sets of solutions of elliptic and parabolic equations

โœ Scribed by Fang-Hua Lin


Publisher
John Wiley and Sons
Year
1991
Tongue
English
Weight
772 KB
Volume
44
Category
Article
ISSN
0010-3640

No coin nor oath required. For personal study only.


๐Ÿ“œ SIMILAR VOLUMES


Nodal Sets and Morse Indices of Solution
โœ Xue-Feng Yang ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 417 KB

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

Existence and Asymptotic-Behavior of Nod
โœ R. Kajikiya ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 533 KB

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\

Starshapedness of Level Sets for Solutio
โœ Elisa Francini ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 277 KB

## 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.

Local estimates for gradients of solutio
โœ O. A. Ladyzhenskaya; N. N. Ural'Tseva ๐Ÿ“‚ Article ๐Ÿ“… 1970 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 1001 KB

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