首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 11 毫秒
1.
We prove, following DiBenedetto’s intrinsic scaling method, that a local bounded weak solution of the equation $$-\sum_{i=1}^{N}\frac{\partial}{\partial x_i}\left[\left| \frac{\partial u}{\partial x_i} \right|^{p_{i}-2} \frac{\partial u}{\partial x_i} \right]=f $$ in Ω, is locally Hölder continuous, where f is a given bounded function and p i  ≥ 2, for any i = 1, . . . , N.  相似文献   

2.
In this paper, we consider nonnegative weak solutions for a class of degenerate parabolic equations. Using Moser’s method, we get the local boundedness of solutions to equations of this class. Then we prove that the solutions are locally Hölder continuous.  相似文献   

3.
We consider a second-order divergence elliptic equation in a domain D divided by a hyperplane in two parts. The equation is uniformly elliptic in one of these parts and is uniformly degenerate with respect to a small parameter ? in the other. We show that each solution is Hölder continuous in D with Hölder exponent independent of ?.  相似文献   

4.
We show that the solutionu of the equation
  相似文献   

5.
We study a second-order elliptic equation for which the Dirichlet problem can be posed in a nonunique way due to the so-called Lavrentiev phenomenon. In the corresponding weighted Sobolev space smooth functions are not dense, which leads to the existence of W – solutions and H – solutions. For H - solutions, we establish the Hölder continuity. We also discuss this question for W – solutions, for which the situation is more complicated.  相似文献   

6.
7.
8.
Summary The Hölder continuity of bounded weak solutions of quasilinear parabolic systems with main part in diagonal form is proved via a parabolic hole-filling technique.This research was supported by the Sonderforschungsbereich 72 of the Deutsche Forschungsgemeinschaft  相似文献   

9.
10.
We prove that the solution map of the $b$ -family equation is Hölder continuous as a map from a bounded set of $H^s(\mathbb{R }), s>\frac{3}{2}$ with $H^r(\mathbb{R })$ ( $0\le r<s$ ) topology, to $C([0, T], H^r(\mathbb{R }))$ for some $T>0$ . Moreover, we show that the obtained exponent of the Hölder continuity is optimal when $s-1<r<s$ .  相似文献   

11.
In this paper we prove the following theorem: Let \(\Omega \subset \mathbb {R}^{n}\) be a bounded open set, \(\psi \in C_{c}^{2}(\mathbb {R}^{n})\), \(\psi > 0\) on \(\partial \Omega \), be given boundary values and u a nonnegative solution to the problem
$$\begin{aligned}&u \in C^{0}(\overline{\Omega }) \cap C^{2}(\{u> 0\}) \\&u = \psi \quad \text { on } \; \partial \Omega \\&{\text {div}} \left( \frac{Du}{\sqrt{1 + |Du|^{2}}}\right) = \frac{\alpha }{u \sqrt{1 + |Du|^{2}}} \quad \text { in } \; \{u > 0\} \end{aligned}$$
where \(\alpha > 0\) is a given constant. Then \(u \in C^{0, \frac{1}{2}} (\overline{\Omega })\). Furthermore we prove strict mean convexity of the free boundary \(\partial \{u = 0\}\) provided \(\partial \{u = 0\}\) is assumed to be of class \(C^{2}\) and \(\alpha \ge 1\).
  相似文献   

12.
In this paper, we study the one-dimensional motion of viscous gas connecting to vacuum state with a jump in density when the viscosity depends on the density. Precisely, when the viscosity coefficient μ is proportional to ρθ and 0 < θ < 1/2, where ρ is the density, the global existence and the uniqueness of weak solutions are proved. This improves the previous results by enlarging the interval of θ.  相似文献   

13.
By means of a minimizing scheme, we constructively define approximate solutions to parabolic systems. On the basis of Campanato theory, these approximate solutions are shown to be locally Hölder equi-continuous with respect to an approximation parameter. As an application, we obtain a weak solution to an initial-boundary value problem with the same Hölder continuity.  相似文献   

14.
15.
In this paper, we prove the Hölder continuity of solutions of parabolic equations containing the p(x, t)-Laplacian. The degree p must satisfy the so-called logarithmic condition.  相似文献   

16.
Annali di Matematica Pura ed Applicata (1923 -) - We consider weak solutions of nonlinear elliptic systems in a $$W^{1,p}$$ -setting which arise as Euler–Lagrange equations of certain...  相似文献   

17.
In the paper, a special class of suitable weak solutions to the three-dimensional nonstationary Navier–Stokes equations is considered, and a reverse H?lder inequality for them is proved. An interesting feature of this class is that it contains solutions having majorants invariant to the Navier-Stokes scaling. Bibliography: titles. Dedicated to Vsevolod Alekseevich Solonnikov Published in Zapiski Nauchnykh Seminarov POMI, Vol. 362, 2008, pp. 325–336.  相似文献   

18.
19.

The authors continue to study the Venttsel' problem, i.e., the boundary-value problem for a parabolic or elliptic equation with the boundary condition in the form of a parabolic or elliptic equation with respect to tangent variables. A priori estimates for the Hölder norms of solutions are established in the case of quasilinear equations of nondivergence form with a quasilinear degenerate boundary Venttsel' condition. Bibliography: 16 titles.

  相似文献   

20.
We consider the following anisotropic Emden–Fowler equation where is a bounded smooth domain and a(x) is a positive smooth function. We investigate the effect of anisotropic coefficient a(x) on the existence of bubbling solutions. We show that at given local maximum points of a(x), there exists arbitrarily many bubbles. As a consequence, the quantity can approach to as . These results show a striking difference with the isotropic case [ Constant].  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号