Boundary value problems for some fully nonlinear elliptic equations
نویسندگان
چکیده
منابع مشابه
Boundary Value Problems for some Fully Nonlinear Elliptic Equations
Let (M, g) be a compact Riemannian manifold of dimension n ≥ 3 with boundary ∂M . We denote the Ricci curvature, scalar curvature, mean curvature, and the second fundamental form by Ric, R , h, and Lαβ , respectively. The Yamabe problem for manifolds with boundary is to find a conformal metric ĝ = eg such that the scalar curvature is constant and the mean curvature is zero. The boundary is call...
متن کاملglobal results on some nonlinear partial differential equations for direct and inverse problems
در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Two-dimensional Nonlinear Boundary Value Problems for Elliptic Equations
Boundary regularity of solutions of the fully nonlinear boundary value problem F(x,u,Du, D2u) = 0 inn, G(x,u, Du) = 0 on dO is discussed for two-dimensional domains Q. The function F is assumed uniformly elliptic and G is assumed to depend (in a nonvacuous manner) on Du. Continuity estimates are proved for first and second derivatives of u under weak hypotheses for smoothness of F, G, and 0. In...
متن کاملOn Neumann Boundary Value Problems for Some Quasilinear Elliptic Equations
We study the role played by the indefinite weight function a(x) on the existence of positive solutions to the problem −div (|∇u|∇u) = λa(x)|u|u+ b(x)|u|u, x ∈ Ω, ∂u ∂n = 0, x ∈ ∂Ω , where Ω is a smooth bounded domain in Rn, b changes sign, 1 < p < N , 1 < γ < Np/(N − p) and γ 6= p. We prove that (i) if ∫ Ω a(x) dx 6= 0 and b satisfies another integral condition, then there exists some λ∗ suc...
متن کاملOn the boundary value problems for fully nonlinear elliptic equations of second order
Fully nonlinear second-order, elliptic equations F (x, u,Du,D2u) = 0 are considered in a bounded domain Ω ⊂ Rn, n ≥ 2. The class of equations includes the Bellman equations supm(L mu+ fm) = 0, where the functions fm and the coefficients of the linear operators Lm are bounded in the Hölder space Cα(Ω), 0 < α < 1. We prove the interior C2,α-smoothness of solutions in Ω with some small α > 0. Unde...
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: 2007
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-006-0072-7