Isolated boundary singularities of semilinear elliptic equations
نویسندگان
چکیده
منابع مشابه
Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations
We investigate quantitative properties of nonnegative solutions u(x) ≥ 0 to the semilinear diffusion equation Lu = f(u), posed in a bounded domain Ω ⊂ R with appropriate homogeneous Dirichlet or outer boundary conditions. The operator L may belong to a quite general class of linear operators that include the standard Laplacian, the two most common definitions of the fractional Laplacian (−∆) (0...
متن کاملAn Inverse Boundary-value Problem for Semilinear Elliptic Equations
We show that in dimension two or greater, a certain equivalence class of the scalar coefficient a(x, u) of the semilinear elliptic equation ∆u + a(x, u) = 0 is uniquely determined by the Dirichlet to Neumann map of the equation on a bounded domain with smooth boundary. We also show that the coefficient a(x, u) can be determined by the Dirichlet to Neumann map under some additional hypotheses.
متن کاملBoundary singularities of solutions to elliptic viscous Hamilton-Jacobi equations
Contents 1 Introduction 2 2 The Dirichlet problem and the boundary trace 7 2. Abstract We study the boundary value problem with measures for (E1) −∆u + g(|∇u|) = 0 in a bounded domain Ω in R N , satisfying (E2) u = µ on ∂Ω and prove that if g ∈ L 1 (1, ∞; t −(2N +1)/N dt) is nondecreasing (E1)-(E2) can be solved with any positive bounded measure. When g(r) ≥ r q with q > 1 we prove that any pos...
متن کاملHardy-Sobolev Critical Elliptic Equations with Boundary Singularities
Unlike the non-singular case s = 0, or the case when 0 belongs to the interior of a domain Ω in IR(n ≥ 3), we show that the value and the attainability of the best Hardy-Sobolev constant on a smooth domain Ω, μs(Ω) := inf {
متن کاملConformally invariant fully nonlinear elliptic equations and isolated singularities
1 Introduction There has been much work on conformally invariant fully nonlinear elliptic equations and applications to geometry and topology. [10], and the references therein. In this and a companion paper [16] we address some analytical issues concerning these equations. For n ≥ 3, consider −∆u = n − 2 2 u n+2 n−2 , on R n .
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: Calculus of Variations and Partial Differential Equations
سال: 2010
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-010-0337-z