Singularities for a 2-Dimensional Semilinear Elliptic Equation with a Non-Lipschitz Nonlinearity
نویسندگان
چکیده
منابع مشابه
A two-phase free boundary problem for a semilinear elliptic equation
In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...
متن کاملHausdorff Dimension of Ruptures for Solutions of a Semilinear Elliptic Equation with Singular Nonlinearity
We consider the following semilinear elliptic equation with singular nonlinearity: u ? 1 u + h(x) = 0 in where > 1; h(x) 2 C 1 (() and is an open subset in R n ; n 2. Let u 2 C 0 (() be a nonnegative nite energy stationary solution and = fx 2 ju(x) = 0g be the rupture set of u. We show that the Hausdorr dimension of is less than or equal to (n?2)+(n+2) +1 .
متن کاملA Semilinear Fourth Order Elliptic Problem with Exponential Nonlinearity
We study a semilinear fourth order elliptic problem with exponential nonlinearity. Motivated by a question raised in [Li], we partially extend known results for the corresponding second order problem. Several new difficulties arise and many problems still remain to be solved. We list the ones we feel particularly interesting in the final section. Mathematics Subject Classification: 35J65; 35J40.
متن کاملa two-phase free boundary problem for a semilinear elliptic equation
in this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $dsubset mathbb{r}^{n}$ with smooth boundary. we give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of caffarelli and friedman regarding the representation of functions whose ...
متن کاملSemilinear fractional elliptic equations with gradient nonlinearity involving measures
We study the existence of solutions to the fractional elliptic equation (E1) (−∆)u + ǫg(|∇u|) = ν in a bounded regular domain Ω of R (N ≥ 2), subject to the condition (E2) u = 0 in Ω, where ǫ = 1 or −1, (−∆) denotes the fractional Laplacian with α ∈ (1/2, 1), ν is a Radon measure and g : R+ 7→ R+ is a continuous function. We prove the existence of weak solutions for problem (E1)-(E2) when g is ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1999
ISSN: 0022-0396
DOI: 10.1006/jdeq.1998.3567