共查询到20条相似文献,搜索用时 31 毫秒
1.
A. A. Arkhipova 《Journal of Mathematical Sciences》2006,132(3):255-273
We consider q-nonlinear nondiagonal elliptic systems, where 1 < q < 2, with strong nonlinear terms in the gradient. Under
a smallness condition on the gradient of a solution in the Morrey space Lq,n−q, we estimate the Lp-norm of the gradient for p > q and the Holder norm of the solution for the case n = 2. An abstract theorem on “quasireverse
Holder inequalities” proved by the author earlier is used essentially. Bibliography: 24 titles.
Dedicated to N. N. Uraltseva on the occasion of her 70th birthday
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 310, 2004, pp. 19–48. 相似文献
2.
《Mathematical Methods in the Applied Sciences》2018,41(1):261-269
In this paper, we study the homogeneous Dirichlet problem for an elliptic equation whose simplest model is where , N≥3 is an open bounded set, θ∈]0,1[, and f belongs to a suitable Morrey space. We will show that the Morrey property of the datum is transmitted to the gradient of a solution. 相似文献
3.
We consider the Cauchy–Dirichlet problem for linear divergence form parabolic operators in bounded Reifenberg flat domain.The coefficients supposed to be only measurable in one of the space variables and small BMO with respect to the others.We obtain Calderón–Zygmund type estimate for the gradient of the solution in generalized weighted Morrey spaces with Muckenhoupt weight. 相似文献
4.
Sun-Sig Byun Dian K. Palagachev 《Calculus of Variations and Partial Differential Equations》2014,49(1-2):37-76
We derive global gradient estimates in Morrey spaces for the weak solutions to discontinuous quasilinear elliptic equations related to important variational problems arising in models of linearly elastic laminates and composite materials. The principal coefficients of the quasilinear operator are supposed to be merely measurable in one variable and to have small-BMO seminorms in the remaining orthogonal directions, and the nonlinear terms are subject to controlled growth conditions with respect to the unknown function and its gradient. The boundary of the domain considered is Reifenberg flat which includes boundaries with rough fractal structure. As outgrowth of the main result we get global Hölder continuity of the weak solution with exact value of the corresponding exponent. 相似文献
5.
We prove that Stein's extension operator preserves Sobolev–Morrey spaces, that is spaces of functions with weak derivatives in Morrey spaces. The analysis concerns classical and generalized Morrey spaces on bounded and unbounded domains with Lipschitz boundaries in the n‐dimensional Euclidean space. 相似文献
6.
In this paper, we show the regularity in Morrey spaces L2, for the gradient of minimizers of quasilinear functionals of the type We allow VMO dependence on the variable x and continuous dependence on the variable u. 相似文献
7.
We obtain a global weighted L p estimate for the gradient of the weak solutions to divergence form elliptic equations with measurable coefficients in a nonsmooth bounded domain. The coefficients are assumed to be merely measurable in one variable and to have small BMO semi-norms in the remaining variables, while the boundary of the domain is supposed to be Reifenberg flat, which goes beyond the category of domains with Lipschitz continuous boundaries. As consequence of the main result, we derive global gradient estimate for the weak solution in the framework of the Morrey spaces which implies global Hölder continuity of the solution. 相似文献
8.
《Mathematische Nachrichten》2017,290(1):37-49
We prove that Burenkov's extension operator preserves Sobolev spaces built on general Morrey spaces, including classical Morrey spaces. The analysis concerns bounded and unbounded open sets with Lipschitz boundaries in the n‐dimensional Euclidean space. 相似文献
9.
We propose results on interior Morrey, BMO and H?lder regularity for the strong solutions to linear elliptic systems of order 2b with discontinuous coefficients and right-hand sides belonging to the Morrey space Lp,λ.
Received: 20 October 2004 相似文献
10.
We obtain global bounds in Lorentz–Morrey spaces for gradients of solutions to a class of quasilinear elliptic equations with low integrability data. The results are then applied to obtain sharp existence results in the framework of Morrey spaces for Riccati type equations with a gradient source term having growths below the natural exponent of the operator involved. A special feature of our results is that they hold under a very general assumption on the nonlinear structure, and under a mild natural restriction on the boundary of the ground domain. 相似文献
11.
Anna L. Mazzucato 《Transactions of the American Mathematical Society》2003,355(4):1297-1364
This paper is devoted to the analysis of function spaces modeled on Besov spaces and their applications to non-linear partial differential equations, with emphasis on the incompressible, isotropic Navier-Stokes system and semi-linear heat equations. Specifically, we consider the class, introduced by Hideo Kozono and Masao Yamazaki, of Besov spaces based on Morrey spaces, which we call Besov-Morrey or BM spaces. We obtain equivalent representations in terms of the Weierstrass semigroup and wavelets, and various embeddings in classical spaces. We then establish pseudo-differential and para-differential estimates. Our results cover non-regular and exotic symbols. Although the heat semigroup is not strongly continuous on Morrey spaces, we show that its action defines an equivalent norm. In particular, homogeneous BM spaces belong to a larger class constructed by Grzegorz Karch to analyze scaling in parabolic equations. We compare Karch's results with those of Kozono and Yamazaki and generalize them by obtaining short-time existence and uniqueness of solutions for arbitrary data with subcritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact, smooth, boundaryless, Riemannian manifolds. BM spaces are defined by means of partitions of unity and coordinate patches, and intrinsically in terms of functions of the Laplace operator.
12.
After establishing the molecule characterization of the Hardy–Morrey space, we prove the boundedness of the singular integral operator and the Riesz potential. We also obtain the Hardy–Morrey space estimates for multilinear operators satisfying certain vanishing moments. As an application, we study the existence and the uniqueness of the solutions to the Navier–Stokes equations for the initial data in the Hardy–Morrey space ????(p?n) for q as small as possible. Here, the Hardy–Morrey space estimates for multilinear operators are important tools. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
13.
We prove monotonicity formulae related to degenerate k-Hessian equations which yield Morrey type estimates for certain integrands involving the second derivatives of the solution.
In the special case k=2 we deduce that weak solutions in , , have locally H?lder continuous gradients. In the nondegenerate case we also show that weak solutions in , , have locally bounded second derivatives.
Received February 25, 1999 / Accepted June 11, 1999 / Published online April 6, 2000 相似文献
14.
We characterize functions in Morrey space by p-Carleson measures. We then reveal a simple relation between Q space and Morrey space, that is Q space can be viewed as a fractional integration of the Morrey space. Therefore, many results for Morrey space can be translated onto Q space. For example, we show that Q space is a dual space by identifying its predual. 相似文献
15.
Jens Frehse 《Israel Journal of Mathematics》1973,15(4):421-429
Letu be a solution of an elliptic (linear or nonlinear) variational inequality with obstacle. Under natural smoothness conditions put upon the data, it is shown that the second derivatives ofu lie in a certain Morrey space and hence, in the case of two independent variables, the solutionu has a Hölder continuous gradient. 相似文献
16.
We consider the Cauchy problem of Navier-Stokes equations in weak Morrey spaces. We first define a class of weak Morrey type spaces Mp*,λ(Rn) on the basis of Lorentz space Lp,∞ = Lp*(Rn)(in particular, Mp*,0(Rn) = Lp,∞, if p > 1), and study some fundamental properties of them; Second,bounded linear operators on weak Morrey spaces, and establish the bilinear estimate in weak Morrey spaces. Finally, by means of Kato's method and the contraction mapping principle, we prove that the Cauchy problem of Navier-Stokes equations in weak Morrey spaces Mp*,λ(Rn) (1<p≤n) is time-global well-posed, provided that the initial data are sufficiently small. Moreover, we also obtain the existence and uniqueness of the self-similar solution for Navier-Stokes equations in these spaces, because the weak Morrey space Mp*,n-p(Rn) can admit the singular initial data with a self-similar structure. Hence this paper generalizes Kato's results. 相似文献
17.
Yoshihiro Sawano 《Mathematische Nachrichten》2010,283(10):1456-1487
The purpose of this paper is to develop a theory of the Besov‐Morrey spaces and the Triebel‐Lizorkin‐Morrey spaces on domains in R n. We consider the pointwise multiplier operator, the trace operator, the extension operator and the diffeomorphism operator. Not only to domains in R n we extend our definition of function spaces to compact oriented Riemannian manifolds. Among the properties above, the result for the trace operator is in particular interesting, which reflects the property of the parameters p, q in the Morrey space ??pq (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
18.
We study the Cauchy problem for the n-dimensional Navier-Stokes equations (n?3), and prove some regularity criteria involving the integrability of the pressure or the pressure gradient for weak solutions in the Morrey, Besov and multiplier spaces. 相似文献
19.
《Stochastic Processes and their Applications》2020,130(8):5006-5036
We study semi-linear elliptic PDEs with polynomial non-linearity in bounded domains and provide a probabilistic representation of their solution using branching diffusion processes. When the non-linearity involves the unknown function but not its derivatives, we extend previous results in the literature by showing that our probabilistic representation provides a solution to the PDE without assuming its existence. In the general case, we derive a new representation of the solution by using marked branching diffusion processes and automatic differentiation formulas to account for the non-linear gradient term. We consider several examples and estimate their solution by using the Monte Carlo method. 相似文献
20.
Rouhuai Wang 《Frontiers of Mathematics in China》2006,1(3):382-429
The main aim of this paper is to discuss the problem concerning the analyticity of the solutions of analytic non-linear elliptic
boundary value problems. It is proved that if the corresponding first variation is regular in Lopatinskiĭ sense, then the
solution is analytic up to the boundary. The method of proof really covers the case that the corresponding first variation
is regularly elliptic in the sense of Douglis-Nirenberg-Volevich, and hence completely generalize the previous result of C.
B. Morrey. The author also discusses linear elliptic boundary value problems for systems of elliptic partial differential
equations where the boundary operators are allowed to have singular integral operators as their coefficients. Combining the
standard Fourier transform technique with analytic continuation argument, the author constructs the Poisson and Green’s kernel
matrices related to the problems discussed and hence obtain some representation formulae to the solutions. Some a priori estimates
of Schauder type and L
p type are obtained.
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Translated from Acta Sci. Natur. Univ. Jilin, 1963, (2): 403–447 by GAO Wenjie. 相似文献