共查询到20条相似文献,搜索用时 0 毫秒
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Patrick Winkert 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(3):289-302
In this paper we prove the L
∞-boundedness of solutions of the quasilinear elliptic equation
$ {ll}
Au \, = f(x,u,\nabla u) &\quad \rm{in }\, \Omega, \\
\dfrac{\partial u}{ \partial \nu} \, = g(x,u) &\quad \rm{on }\, \partial \Omega,
$ \begin{array}{ll}
Au \, = f(x,u,\nabla u) &\quad \rm{in }\, \Omega, \\
\dfrac{\partial u}{ \partial \nu} \, = g(x,u) &\quad \rm{on }\, \partial \Omega,
\end{array} 相似文献
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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8.
Magnus Fontes 《偏微分方程通讯》2013,38(3-4):681-702
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The solvability of the fully nonlinear stationary Venttsel' problem is established. The equation and the boundary condition are assumed to be uniformly elliptic. Bibliography: 12 titles. Translated fromProblemy Matematicheskogo Analiza, No. 19, 1999, pp. 3–26. 相似文献
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We establish the local Hölder continuity for the nonnegative weak solutions of certain doubly nonlinear parabolic equations possessing a singularity in the time derivative part and a degeneracy in the principal part. The proof involves the method of intrinsic scaling and the setting is a measure space equipped with a doubling non-trivial Borel measure supporting a Poincaré inequality. 相似文献
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A. V. Ivanov 《Journal of Mathematical Sciences》1991,56(2):2320-2347
For positive bounded generalized solutions of degenerate parabolic equations of the form t 0, m 2, one establishes local Hölder estimates, independent of the lower bounds of the indicated solutions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 171, pp. 70–105, 1989. 相似文献
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M. Kubo K. Shirakawa N. Yamazaki 《Journal of Mathematical Analysis and Applications》2012,387(2):490-511
We create a general framework for mathematical study of variational inequalities for a system of elliptic–parabolic equations. In this paper, we establish a solvability theorem concerning the existence of solutions for the vector-valued elliptic–parabolic variational inequality with time-dependent constraint. Moreover, we give some applications of the system, for example, time-dependent boundary obstacle problem and time-dependent interior obstacle problem. 相似文献
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Xinfu Chen 《应用数学学报(英文版)》1987,3(1):70-96
Consider the degenerate parabolic equations of the type $$u_t = div A(x,t,u,Du) + b(x,t,u,Du)$$ which is of the same nature as $$u_t = div|Du|^p Du + |Du|^{p + 2} (p > 2).$$ This paper is to study the \(C^{1 + \alpha } ,\frac{{1 + \alpha }}{2}\) Hölder continuity of a class of degenerate parabolic equations and the existence and uniqueness of the initial boundary value problem. 相似文献
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We provide a geometric Poincaré type formula for stable solutions of ?Δ p (u) = f(u). From this, we derive a symmetry result in the plane. This work is a refinement of previous results obtained by the authors under further integrability and regularity assumptions. 相似文献
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Marcus Stiemer 《Numerische Mathematik》2010,116(3):435-462
In this article boundary value problems for partial differential equations of mixed elliptic–parabolic type are considered.
To ensure that the considered problems possess a unique solution, the usual variational existence proof for parabolic problems
is extended to the mixed situation. Further, the convergence of approximations computed by a time-space Galerkin method to
the solution of the mixed problem is proven and error estimates are given. 相似文献
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Seonghak Kim Baisheng Yan 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(1):65-100
We investigate the existence and properties of Lipschitz solutions for some forward–backward parabolic equations in all dimensions. Our main approach to existence is motivated by reformulating such equations into partial differential inclusions and relies on a Baire's category method. In this way, the existence of infinitely many Lipschitz solutions to certain initial-boundary value problem of those equations is guaranteed under a pivotal density condition. Under this framework, we study two important cases of forward–backward anisotropic diffusion in which the density condition can be realized and therefore the existence results follow together with micro-oscillatory behavior of solutions. The first case is a generalization of the Perona–Malik model in image processing and the other that of Höllig's model related to the Clausius–Duhem inequality in the second law of thermodynamics. 相似文献
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Longtime behavior of degenerate equations with the nonlinearity of polynomial growth of arbitrary order on the whole space RN is considered. By using -trajectories methods, we proved that weak solutions generated by degenerate equations possess an (LU2 (RN), Lloc2 (RN))-global attractor. Moreover, the upper bounds of the Kolmogorov ε-entropy for such global attractor are also obtained. 相似文献
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