共查询到20条相似文献,搜索用时 829 毫秒
1.
Bian Baojun 《偏微分方程(英文版)》1991,4(1)
We consider the problem of existence for viscosity solutions of seoond order fully nonlinear elliptic partial differential equations F(D²u, Du, u, z) = 0. We prove existence results for viscosity solutions in W^{1,∞} under assumptions that function F satisfies the natural structure conditions. We do not assume F is convex. 相似文献
2.
W2,ploc(\Omega)\cap C1,α(\bar Ω) Viscosity Solutions of Neumann Problems for Fully Nonlinear Elliptic Equations 下载免费PDF全文
Jiguang Bao 《偏微分方程(英文版)》1995,8(3):219-232
In this paper we study fully nonlinear elliptic equations F(D²u, x) = 0 in Ω ⊂ R^n with Neumann boundary conditions \frac{∂u}{∂v} = a(x)u under the rather mild structure conditions and without the concavity condition. We establish the global C^{1,Ω} estimates and the interior W^{2,p} estimates for W^{2,q}(Ω) solutions (q > 2n) by introducing new independent variables, and moreover prove the existence of W^{2,p}_{loc}(Ω)∩ C^{1,α}(\bar \Omega} viscosity solutions by using the accretive operator methods, where p E (0, 2), α ∈ (0, 1}. 相似文献
3.
The Obstacle Problems for Second Order Fully Nonlinear Elliptic Equations with Neumann Boundary Conditions 下载免费PDF全文
Bao Jiguang 《偏微分方程(英文版)》1992,5(3)
In this paper we prove the existence theorem of the strong solutions to the obstacle problems for second order fully nonlinear elliptic equations with the Neumann boundary conditions F(x, u, Du, D²u) ≥ 0, x ∈ Ω u ≤ g, x ∈ Ω (u - g)F(x, u, Du, D²u) = 0, x ∈ Ω D_vu = φ(x, u), x ∈ ∂Ω where F(x, z, p, r) satisfies the natural structure conditions and is concave with respect to r, p, and φ(x, z) is nondecreasing in z, and g(x) satisfies the consistency condition. 相似文献
4.
C1,α Regularity of Viscosity Solutions of Fully Nonlinear Elliptic PDE Under Natural Structure Conditions 下载免费PDF全文
Chen Yazhe 《偏微分方程(英文版)》1993,6(3):193-216
In this paper we are concemed with fully nonlinear elliptic equation F(x, u, Du, D²u) = 0. We establish the interior Lipschitz continuity and C^{1,α} regularity of viscosity solutions under natural structure conditions without differentiating the equation as usual, especially we give a new analytic Harnack inequality approach to C^{1,α} estimate for viscosity solutions instead of the geometric approach given by L. Caffarelli \& L. Wang and improve their results. Our structure conditions are rather mild. 相似文献
5.
Nonlinear Degenerate Oblique Boundary Value Problems for Second Order Fully Nonlinear Elliptic Equations 下载免费PDF全文
Bao Jiguang 《偏微分方程(英文版)》1990,3(2)
In this paper we study the existence theorem for solution of the nonlinear degenerate oblique boundary value problems for second order fully nonlinear elliptic equations F(x, u, Du, D²u) = 0 \quad x ∈ Ω, G(x, u, D, u) = 0, \qquad x ∈ ∂Ω where F (x, z, p, r) satisfies the natural structure conditions, G (x, z, q) satisfies G_q ≥ 0, G_x ≤ - G_0 < 0 and some structure conditions, vector τ is nowhere tangential to ∂Ω. This result extends the works of Lieberman G. M., Trudinger N. S. [2], Zhu Rujln [1] and Wang Feng [6]. 相似文献
6.
Ning Zhu 《偏微分方程(英文版)》2002,15(4):1-12
In this paper, we deal with the following fully nonlinear partial differential equation of parabolic type F(x, t, u,Du,D²u) + u_t = 0 in Q_T with the third boundary value conditions. We prove that under some structure conditions on F, the W^{2,1}_p (p > 3N + 1) strong solutions for the problem have the ^{1,0}_∞ a priori estimates. 相似文献
7.
A Note on C1,α Estimates for Solutions of Fully Nonlinear Elliptic Equations and Obstacle Problems 下载免费PDF全文
Chen Yazhe 《偏微分方程(英文版)》1992,5(4):1-12
We deal with C^{1,α} interior estimates for solutions of fully nonlinear equation F(D²u, Du, x) = f(x) with the bounded gradient Du and a bounded f(x). Based on these estimates we obtain the existence of strong solutions of the obstacle problem for fully nonlinear elliptic equations under natural structure conditions. 相似文献
8.
Chen Yazhe 《偏微分方程(英文版)》1991,4(3)
In this paper we obtain the existence of W^{2, ∞} solutions of the obstacle problems for fully nonlinear elliptic equations under more general structure conditions than those in [1] by using the mollifier approach, which is also extended in our discussion. 相似文献
9.
C1,α Regularity of Viscosity Solutions of Fully Nonlinear Parabolic PDE Under Natural Structure Conditions 下载免费PDF全文
Ge Han 《偏微分方程(英文版)》1999,12(1):1-10
In this paper, we concern the fully nonlinear parabolic equations u_t + F(x, t , u, Du, D² u) = 0. Under the natural structure conditions as that in [1], we obtain the C^{1,\alpha} estimates of the viscosity solutions. 相似文献
10.
Yang Xiang 《偏微分方程(英文版)》1997,10(2):107-122
This paper is concerned with the comparison principle for viscosity solutions of the nonlinear elliptic equation F(Du, D²u} + |u|^{s-1}u =f in R^N, where f is uniformly continuous and F satisfies some conditions about p (p > 2}. We got the comparison principle for the viscosity solutions with some high growth at infinity, which relies on the relation between p and s. 相似文献
11.
Wang Junyu 《偏微分方程(英文版)》1990,3(3)
ln this paper we consider the model problem for a second order quasilinear degenerate parabolic equation {D_xG(u) = t^{2N-1}D²_xK(u) + t^{N-1}D_x,F(u) \quad for \quad x ∈ R,t > 0 u(x,0) = A \quad for \quad x < 0, u(x,0) = B \quad for \quad x > 0 where A < B, and N > O are given constants; K(u) =^{def} ∫^u_Ak(s)ds, G(u)=^{def} ∫^u_Ag(s)ds, and F(u) =^{def} ∫^u_Af(s)ds are real-valued absolutely continuous functions defined on [A, B] such that K(u) is increasing, G(u) strictly increasing, and \frac{F(B)}{G(B)}G(u) - F(u) nonnegative on [A, B]. We show that the model problem has a unique discontinuous solution u_0 (x, t) when k(s) possesses at least one interval of degeneracy in [A, B] and that on each curve of discontinuity, x = z_j(t) =^{def} s_jt^N, where s_j= const., j=l,2, …, u_0(x, t) must satisfy the following jump conditions, 1°. u_0(z_j(t) - 0, t) = a_j, u_0 (z_j(t) + 0, t) = b_j, and u_0(z_j(t) - 0, t) = [a_j, b_j] where {[a_j, b_j]; j = 1, 2, …} is the collection of all intervals of degeneracy possessed by k (s) in [A, B], that is, k(s) = 0 a. e. on [a_j, b_j], j = 1, 2, …, and k(s) > 0 a. e. in [A, B] \U_j[a_j, b_j], and 2°. (z_j(t)G(u_0(x, t)) + t^{2N-1}D_xK(u_0(x, t)) + t^{N-1}F(u_0(x, t)))|\frac{s=s_j+0}{s=s_j-0} = 0 相似文献
12.
本文研究了R^N中的非线性退化椭圆型方程F(Du,D^2u)+us=f的非负粘性解的存在性,其中s〉0,F满足某些关于p的条件,本文在下面的条件下证明了存在性;1.s〉p-1,f在无穷远处不需要增长条件;2.0〈s≤p-1,f在无穷远处具有某种增长条件。 相似文献
13.
In two-space-dimensional case we get the sharp lower bound of the life-span of classical solutions to the Cauchy problem with small initial data for fully nonlinear wave equations of the form ◻u = F (u, Du, D_zDu) in which F(\hat{λ}) = O(|\hat{λ}|^{1+α}) with α = 2 in a neighbourhood of \hat{λ} = 0. The cases α = 1 and α ≥ 3 have been considered respectively in [1] and [2]. 相似文献
14.
Yin Jingxue 《偏微分方程(英文版)》1990,3(4)
In this paper we study the first boundary value problem for nonlinear diffusion equation \frac{∂u}{∂t} + \frac{∂}{∂x}f(u) = \frac{∂}{∂x}A(\frac{∂}{∂x}B(u)) whereA(s) = ∫¹_0a(σ)dσ, B(s) = ∫¹_0b(σ)dσ with a(s) ≥ 0, b(s) ≥ 0. We prove the existence of BV solutions under the much general structural conditions lim_{s → + ∞} A(s) = +∞, lim_{s → - ∞} A(s) = -∞ Moreover, we show the uniqueness without any structural conditions. 相似文献
15.
The Dirichlet Problems for a Class of Fully Nonlinear Elliptic Equations Relative to the Eigenvalues of the Hessian 下载免费PDF全文
Wang Lianju 《偏微分方程(英文版)》1992,5(2)
ln this paper we discuss the Dirichlet problems for a class of fully nonliucar elliptic equations F(D² u) = ψ(x, u)(ψ(x, u, ∇u)) \quad in Q u = φ(x) \quad on ∂Ω where F is represented by a symmetric function f(λ_1, …, λ_n) of the eigenvalues (λ_1, …,λ_n) of the Hessian D²u. This result extends the works of Caffarelli L., Nirenberg L., Spruck L. [2] to more general cases. 相似文献
16.
In this paper we study the initial boundary value problem of GBBM equations on unbounded domain u_t - Δu_t = div f(u) u(x,0) = u_0(x) u|_{∂Ω} = 0 and corresponding Cauchy problem. Under the conditions: f( s) ∈ C^sup1 and satisfies (H)\qquad |f'(s)| ≤ C|s|^ϒ, 0 ≤ ϒ ≤ \frac{2}{n-2} if n ≥ 3; 0 ≤ ϒ < ∞ if n = 2 u_0(x) ∈ W^{2,p}(Ω) ∩ W^{2,2}(Ω) ∩ W^{1,p}_0(Ω)(W^{2,p}(R^n) ∩ W^{2,2}(R^n) for Cauchy problem), 2 ≤ p < ∞, we obtain the existence and uniqueness of global solution u(x, t) ∈ W^{1,∞}(0, T; W^{2,p}(Ω) ∩ W^{2,2}(Ω) ∩ W^{1,p}_0(Ω))(W^{1,∞}(0, T; W^{2,p}(R^n) ∩ W^{2,2} (R^n)) for Cauchy problem), so the results of [1] and [2] are generalized and improved in essential. 相似文献
17.
Local W^{1,q} estimates for weak solutions to a class of equations in divergence form D_i(a_{ij}(x)|Du|^{p-2D_ju) = 0 are obtained, where q > p is given. These estimates are very important in obtaining higher regularity for the weak solutions to elliptic equations. 相似文献
18.
Regularity Results for Nonlinear Systems of Partial Differential Equations Under Weak Ellipticity Conditions 下载免费PDF全文
Yuesheng Zeng 《偏微分方程(英文版)》2000,13(3):217-225
We prove C^{1,α} almost everywhere regularity for weak solutions in the space W^{1,k} (Ω, R^N) of the systems - D_αA^i_α(x,u,Du) = B^i(z,u,Du) under the weak ellipticity condition ∫A(x_0 ,u, p + DΦ) ⋅ DΦdy ≥ λ ∫ (|DΦ|² + |DΦ|^k)dy. 相似文献
19.
Prof.Dr. Wolf von Wahl 《manuscripta mathematica》1974,13(2):187-206
This paper deals with the question of the existence of classical solutions for the equations $$\frac{{\partial ^{2} u}{\partial t^{2} }} + \sum_{\begin{subarray}{l} |\alpha| \leqslant m \\ | \beta | \leqslant m \end{subarray}} D^{\alpha} (A_{\alpha \beta } (x,t) D^{\beta} u) = f (t,x,u)$$ on [0,T] × G. G is a bounded or unbounded domain; the differential operator in the space variables is elliptic; the initial values of u are prescribed and Dαu (t,x) vanishes for (t,x) ∈ [0,T] × ?G, |α|≤ m?1. First we develop a method for solving regularly linear wave equations. In contrast to the usual compatibility conditions, our method requires less differentiability in t but imposes some boundary conditions on f(t). It allows some applications to nonlinear problems which will be treated in the second part of this paper and which e.g. enable us to solve ?2 u/?t2?A(t)u+u3=f. 相似文献
20.
Kjell-Ove Widman 《manuscripta mathematica》1971,5(4):299-308
The purpose of this note is to observe that a variant of the method of Morrey, as exposed in [4] and [5], can be used to show that weak solutions of a certain class of elliptic systems of quasilinear equations of arbitrary order of the form $$\mathop {\sum\limits_{\left| \alpha \right| \leqslant m} {( - 1)^{\left| \alpha \right|} D^\alpha F_{\alpha ,v} (x,u,Du, \ldots ,D^m u) = 0,v = 1,2 \ldots ,N} }\limits_{u = (u_1 ,u_2 , \ldots ,u_{N)} } $$ are Hölder continuous, thus partially extending results of Lady?enskaja-Ural'ceva [3] and Serrin [8] to higher order equations. A full extension is not possible. With suitable assumptions the Hölder continuity holds out to the boundary. 相似文献