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1.
Pietro Zamboni 《manuscripta mathematica》2000,102(3):311-323
In this note we prove the Harnack inequality for non negative solutions of the quasilinear equation
under very general structural assumptions satisfied by functions A and B.
Received: 25 March 1999/ Revised version: 18 February 2000 相似文献
2.
Mountain pass type solutions for quasilinear elliptic equations 总被引:4,自引:0,他引:4
Ph. Clément M. García-Huidobro R. Manásevich K. Schmitt 《Calculus of Variations and Partial Differential Equations》2000,11(1):33-62
We establish the existence of weak solutions in an Orlicz-Sobolev space to the Dirichlet problem
where is a bounded domain in , , and the function is an increasing homeomorphism from onto . Under appropriate conditions on , , and the Orlicz-Sobolev conjugate of (conditions which reduce to subcriticality and superlinearity conditions in the case the functions are given by powers),
we obtain the existence of nontrivial solutions which are of mountain pass type.
Received April 22, 1999 / Accepted June 11, 1999 / Published online April 6, 2000 相似文献
3.
Bernard Dacorogna Irene Fonseca 《Calculus of Variations and Partial Differential Equations》2002,14(2):115-149
The study of existence of solutions of boundary-value problems for differential inclusions
where , is an open subset of , is a compact set, and B is a -valued first order differential operator, is undertaken. As an application, minima of the energy for large magnetic bodies
where the magnetization is taken with values on the unit sphere is the induced magnetic field satisfying and is the anisotropic energy density, and the applied external magnetic field is given by , are fully characterized. Setting with , it is shown that E admits a minimizer with if and only if either 0 is on a face of or , where denotes the convex hull of Z.
Received: 6 November 2000 / Accepted: 23 January 2001 / Published online: 23 April 2001 相似文献
4.
Maciej Kocan 《Numerische Mathematik》1995,72(1):73-92
Summary.
We obtain estimates on the minimal size of an
equally spaced grid which can be used to construct monotone
and consistent approximations to elliptic problems. The
estimates are given in terms of the ellipticity of the
equation. This problem is related to diophantine
approximations, see the Appendix written by W. M. Schmidt.
Received January 10, 1995 相似文献
5.
In this paper, by using the fixed point theory, we obtain a new existence result for bounded positive solutions of the quasilinear elliptic equations in two-dimensional exterior domains. 相似文献
6.
Paolo Cianci 《Applicable analysis》2013,92(4):429-437
We establish the boundedness of solutions of Dirichlet Problem for a class of degenerate nonlinear elliptic equations. To prove the result we follow a modification of Moser's method. 相似文献
7.
M. T. Karaev 《Monatshefte für Mathematik》2008,155(2):161-166
In this article we give, in terms of so-called Berezin symbols, some necessary conditions for the solvability of the Riccati
equation
on the set
of all Toeplitz operators on the Hardy space
.
Author’s address: Department of Technical Programs, Isparta (MYO) Vocational School, Suleyman Demirel University, 32260 Isparta,
Turkey 相似文献
8.
9.
10.
In this paper, by using fixed point theory, under quite general conditions on the nonlinear term, we obtain an existence result on unbounded positive solutions of certain quasilinear elliptic equations in two-dimensional exterior domains. 相似文献
11.
This paper is devoted to the study of the following degenerate Neumann problem for a quasilinear elliptic integro-differential operator Here is a second-order elliptic integro-differential operator of Waldenfels type and is a first-order Ventcel' operator with a(x) and b(x) being non-negative smooth functions on such that on . Classical existence and uniqueness results in the framework of H?lder spaces are derived under suitable regularity and structure conditions on the nonlinear term f(x,u,Du). Received April 22, 1997; in final form March 16, 1998 相似文献
12.
We prove regularity results for solutions to a class of quasilinear elliptic equations in divergence form in the Heisenberg
group . The model case is the non-degenerate p-Laplacean operator where , and p is not too far from 2. 相似文献
13.
14.
Boundary regularity for nonlinear elliptic systems 总被引:3,自引:0,他引:3
J.F. Grotowski 《Calculus of Variations and Partial Differential Equations》2002,15(3):353-388
We consider questions of boundary regularity for solutions of certain systems of second-order nonlinear elliptic equations.
We obtain a general criterion for a weak solution to be regular in the neighbourhood of a given boundary point. The proof
yields directly the optimal regularity for the solution in this neighbourhood. This result is new for the situation under
consideration (general nonlinear second order systems in divergence form, with inhomogeneity obeying the natural growth conditions).
Received: 6 July 2001 / Accepted: 27 September 2001 / Published online: 28 February 2002 相似文献
15.
We prove the existence of solutions of nonlinear elliptic equations with first-order terms having “natural growth” with respect
to the gradient. The assumptions on the source terms lead to the existence of possibly unbounded solutions (though with exponential
integrability). The domain Ω is allowed to have infinite Lebesgue measure.
Received: April 13, 2001; in final form: September 29, 2001?Published online: July 9, 2002 相似文献
16.
We introduce a new concept of solution for the Dirichlet problem for quasilinear parabolic equations in divergent form for
which the energy functional has linear growth. Using Kruzhkov's method of doubling variables both in space and time we prove
uniqueness and a comparison principle in for these solutions. To prove the existence we use the nonlinear semigroup theory.
Received: 26 October 2000 / Revised version: 1 May 2001 / Published online: 24 September 2001 相似文献
17.
We prove that the composition S(u1, …, un) of a multilinear multiple 2-summing operator S with 2-summing linear operators uj is nuclear, generalizing a linear result of Grothendieck.
Both authors were partially supported by DGICYT grant BMF2001-1284. 相似文献
18.
The main goal of this paper is to prove existence and comparison results for elliptic differential inclusions governed by a quasilinear elliptic operator and a multivalued function given by Clarke’s generalized gradient of some locally Lipschitz function. These kinds of problems have been treated in the past by various authors including the authors of this paper. However, in all the works we are aware of, additional assumptions on the structure of the elliptic operator and/or the generalized Clarke’s gradient are needed to get comparison results in terms of sub-supersolutions. Comparison principles were obtained recently, e.g., in the case where the elliptic operator is of potential type, or Clarke’s gradient is required to satisfy some one-sided growth condition, or the sub-supersolutions are supposed to satisfy additional properties. The novelty of this paper is that we are able to obtain a comparison principle without assuming any of the above restrictions. To the best of our knowledge this is the first mathematical treatment of the considered elliptic inclusion in its full generality. The obtained results of this paper complement the development of the sub-supersolution method for nonsmooth problems presented in a recent monograph by S. Carl, Vy K. Le and D. Motreanu. 相似文献
19.
Xi-Nan Ma 《Mathematische Zeitschrift》2002,240(1):1-11
We study solutions of the nonlinear elliptic equation on a bounded domain in . It is shown that the set of points where the graph of the solution has negative Gauss curvature always extends to the boundary, unless it is empty.
The meethod uses an elliptic equation satisfied by an auxiliary function given by the product of the Hessian determinant and
a suitable power of the solutions. As a consequence of the result, we give a new proof for power concavity of solutions to
certain semilinear boundary value problems in convex domains.
Received: 12 January 2000; in final form: 15 March 2001 / Published online: 4 April 2002 相似文献
20.
This paper studies, under some natural monotonicity conditions, the theory (existence and uniqueness, a priori estimate,
continuous dependence on a parameter) of forward–backward stochastic differential equations and their connection with quasilinear
parabolic partial differential equations. We use a purely probabilistic approach, and allow the forward equation to be degenerate.
Received: 12 May 1997 / Revised version: 10 January 1999 相似文献