Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0653.35027
Díaz, J.I.
Applications of symmetric rearrangement to certain nonlinear elliptic equations with a free boundary. (English)
[A] Nonlinear differential equations, Lect. 7th Congr., Granada/Spain 1984, Res. Notes Math. 132, 155-181 (1985).

[For the entire collection see Zbl 0638.00015.] \par Consider a nonlinear elliptic equation of the type $$ (1)\quad - Lu+f(u)=g\quad in\quad \Omega;\quad u=h\quad on\quad \partial \Omega$$ where $\Omega$ is a regular bounded open set of R N, L is a linear elliptic second order operator $$ Lu=\sum\sp{N}\sb{i,j=1}(\partial /\partial x\sb j)(a\sb{ij}(x)(\partial u/\partial x\sb i))+\sum\sp{N}\sb{j=1\quad}(\partial /\partial x\sb j)(b\sb j(x)u)+c(x)u. $$ (1) appears in many different contexts: in the study of isothermal chemical reactions, of stationary solutions of many nonlinear evolution equations, and others. Many authors considered the existence and properties of a free boundary F(u) for solutions of (1). The author in this paper obtains some qualitative properties in F(u) using symmetric rearrangement of a function in the sense of Hardy and Littlewood.
[J.H.Tian]

MSC 2000:: *35J65 (Nonlinear) BVP for (non)linear elliptic equations
35R35 Free boundary problems for PDE

Keywords: symmetric rearrangement; nonlinear elliptic equations; isothermal chemical reactions; stationary solutions; free boundary

Citations: Zbl 0638.00015

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]