共查询到20条相似文献,搜索用时 0 毫秒
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Ya. Belopolskaya 《Journal of Mathematical Sciences》1998,92(6):4256-4272
A class of nondiagonal systems of nonlinear parabolic equations that can be reduced to a scalar parabolic equation in the
phase space of a larger dimension is described. In view of such a reduction, it is possible to state the maximum principle
for solutions to systems of nonlinear parabolic equations and derive a priori C2+α-estimates for a solution to the Cauchy problem. Bibliography: 19 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 16. 1997, pp. 41–67. 相似文献
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Markus Biegert 《manuscripta mathematica》2010,133(3-4):273-306
The purpose of this paper is to prove a priori estimates for the difference of weak solutions to certain quasi-linear elliptic equations, where the p(x)-Laplace operator serves as a prototype for our method. 相似文献
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Gerhard Kristensson Niklas Wellander 《Mathematical Methods in the Applied Sciences》2015,38(11):2194-2215
In this paper, we present a collection of a priori estimates of the electromagnetic field scattered by a general bounded domain. The constitutive relations of the scatterer are in general anisotropic. Surface averages are investigated, and several results on the decay of these averages are presented. The norm of the exterior Calderón operator for a sphere is investigated and depicted as a function of the frequency. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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A. Alexandrou Himonas Gerard Misiolek 《Proceedings of the American Mathematical Society》2002,130(10):3043-3050
We present an elementary proof of an a priori estimate of Bourgain for a general class of multipliers on a circle using an extension of methods developed in our previous work. The main tool is a suitable version of a counting argument of Zygmund for unbounded regions.
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Guozhen Lu Peiyong Wang Jiuyi Zhu 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2012
Liouville-type theorems are powerful tools in partial differential equations. Boundedness assumptions of solutions are often imposed in deriving such Liouville-type theorems. In this paper, we establish some Liouville-type theorems without the boundedness assumption of nonnegative solutions to certain classes of elliptic equations and systems. Using a rescaling technique and doubling lemma developed recently in Polá?ik et al. (2007) [20], we improve several Liouville-type theorems in higher order elliptic equations, some semilinear equations and elliptic systems. More specifically, we remove the boundedness assumption of the solutions which is required in the proofs of the corresponding Liouville-type theorems in the recent literature. Moreover, we also investigate the singularity and decay estimates of higher order elliptic equations. 相似文献
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A. V. Ivanov 《Journal of Mathematical Sciences》1978,10(1):44-53
Local estimates on the boundary of a domain for the gradients of solutions of second-order quasilinear elliptic equations are constructed. These estimates are applied to establish local estimates on the boundary for the second derivatives of solutions of a certain class of second-order nonlinear elliptic equations.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 69, pp. 65–76, 1977. 相似文献
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G. G. Laptev 《Mathematical Notes》1998,64(4):488-495
We study an initial boundary value problem for the semilinear parabolic equation
where the left-hand side is a linear uniformly parabolic operator of order 2b. We prove sufficient growth conditions on the functionƒ with respect to the variablesu, Du,, D
2b–1
u, such that the apriori estimate of the norm of the solution in the Sobolev spaceW
p
2b,1
is expressible in terms of the low-order norm in the Lebesgue space of integrable functionsL
l,m
.Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 564–572, October, 1998.In conclusion, the author wishes to thank his scientific adviser, corresponding member of the Russian Academy of Sciences S. I. Pokhozhaev, for setting the problem and useful discussions of the results, and also Ya. Sh. Il'yasov for valuable remarks.This research was supported by the Russian Foundation for Basic Research under grant No. 96-15-96102. 相似文献
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A. V. Ivanov 《Journal of Mathematical Sciences》1978,10(2):217-240
We consider classes of elliptic equations of the form (x,u,u
D
2
u)=0 for the solutions of which one establishes local and global a priori estimates for D
2
u=. In particular, one investigates the Monge-Ampere equation, and for its convex solutions one constructs a local and a global estimate for D
2
u and a local estimate for.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 59, pp. 31–59, 1976. 相似文献
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Ar. S. Tersenov 《Siberian Mathematical Journal》2012,53(3):539-550
Under consideration is the Dirichlet problem for singular anisotropic elliptic equations with a nonlinear source. Some new a priori estimates are obtained, implying that the solvability of the Dirichlet problem in the class of bounded solutions essentially depends on the dimension of the domain of the problem. 相似文献
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I. V. Astashova 《Proceedings of the Steklov Institute of Mathematics》2008,261(1):22-33
For a higher order quasilinear differential equation, the existence of uniform estimates for positive solutions with common domain of definition is proved; these estimates depend on the estimates for the coefficients of the equation and do not depend on the coefficients themselves. 相似文献
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We study the equation (λ+H)u=f whereH is a self-adjoint operator associated with the Dirichlet form inL
2(IR
d
,pdx). A priori estimates of the first and the second order derivatives of solutions are obtained under minimal restrictions on
the coefficients of the operator and measure. As a consequence we give a criterion of the essential self-adjointness of the
operatorH ↾C
0
∞
(IR
d
) with non-smooth coefficients.
Recipient of a Dov Biegun Postdoctoral Fellowship. 相似文献
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CAO Yi LI DongSheng & WANG LiHe College of Science Xi’an Jiaotong University Xi’an China Department of Mathematics The University of Iowa Iowa City IA - USA 《中国科学 数学(英文版)》2011,(3):457-462
For the fully nonlinear uniformly elliptic equation F(D2u) = 0, it is well known that the viscosity solutions are C2,α if the nonlinear operator F is convex (or concave). In this paper, we study the classical solutions for the fully nonlinear elliptic equation where the nonlinear operator F is locally C1,β a.e. for any 0 < β < 1. We will prove that the classical solutions u are C2,α. Moreover, the C2,α norm of u depends on n,F and the continuous modulus of D2u. 相似文献
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We study the relativistic Euler equations on the Minkowski spacetime background. We make assumptions on the equation of state and the initial data that are relativistic analogs of the well-known physical vacuum boundary condition, which has played an important role in prior work on the non-relativistic compressible Euler equations. Our main result is the derivation, relative to Lagrangian (also known as co-moving) coordinates, of local-in-time a priori estimates for the solution. The solution features a fluid-vacuum boundary, transported by the fluid four-velocity, along which the hyperbolicity of the equations degenerates. In this context, the relativistic Euler equations are equivalent to a degenerate quasilinear hyperbolic wave-map-like system that cannot be treated using standard energy methods. 相似文献
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Sungwon Cho 《Journal of Differential Equations》2010,248(4):820-836
We evaluate the rate of decay for solutions to second order parabolic equations, which vanish on the boundary, while the right-hand side is allowed to be unbounded. Our approach is based on a special growth lemma, and it works for both divergence and non-divergence equations, in domains satisfying a general “exterior measure condition” (A). The result for elliptic case is published in Cho and Safonov (2007) [2]. 相似文献