共查询到20条相似文献,搜索用时 15 毫秒
1.
Linfeng Mei 《Journal of Mathematical Analysis and Applications》2008,339(2):1294-1304
This paper considers positive solutions to problem
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Hongjie Dong Hong Zhang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(4):971-992
We obtain Dini type estimates for a class of concave fully nonlinear nonlocal elliptic equations of order with rough and non-symmetric kernels. The proof is based on a novel application of Campanato's approach and a refined estimate in [9]. 相似文献
4.
Given a bounded domain Ω in RN, and a function a∈Lq(Ω) with q>N/2, we study the existence of a positive solution for the quasilinear problem
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A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirichlet problems
We consider the 2m-th order elliptic boundary value problem Lu = f (x, u) on a bounded smooth domain with Dirichlet boundary conditions on ∂Ω. The operator L is a uniformly elliptic operator of order 2m given by . For the nonlinearity we assume that , where are positive functions and q > 1 if N ≤ 2m, if N > 2m. We prove a priori bounds, i.e, we show that for every solution u, where C > 0 is a constant. The solutions are allowed to be sign-changing. The proof is done by a blow-up argument which relies on
the following new Liouville-type theorem on a half-space: if u is a classical, bounded, non-negative solution of ( − Δ)
m
u = u
q
in with Dirichlet boundary conditions on and q > 1 if N ≤ 2m, if N > 2m then .
相似文献
6.
In this paper, we prove a Hadamard property and Liouville type theorems for viscosity solutions of fully nonlinear elliptic partial differential equations with a gradient term, both in the whole space and in an exterior domain. 相似文献
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We consider transformations of the (metric) Quadratic Assignment Problem (QAP) that exploit the metric structure of a given instance. We show in particular how the structural properties of rectangular grids can be used to improve a given lower bound. Our work is motivated by previous research of Palubetskes (1988), and it extends a bounding approach proposed by Chakrapani and Skorin-Kapov (1993). Our computational results indicate that the present approach is practical; it has been applied to problems of dimension up ton = 150. Moreover, the new approach yields by far the best lower bounds on most of the instances of metric QAPs that we considered.The authors gratefully acknowledge financial support by the Christian Doppler Laboratorium für Diskrete Optimierung. 相似文献
9.
Antonio Tarsia 《Journal of Global Optimization》2008,40(1-3):443-453
We give a short survey of the Campanato near operators theory and of its applications to fully nonlinear elliptic equations. 相似文献
10.
Jingxue Yin Jing Li Chunhua Jin 《Journal of Mathematical Analysis and Applications》2009,360(1):119-129
This paper is concerned with the existence and comparison principle of classical solutions for a class of fully nonlinear degenerate parabolic equations. 相似文献
11.
Philip W. Schaefer 《Expositiones Mathematicae》2006,24(4):371-377
A priori bounds are determined for certain energy expressions for a class of semi-linear parabolic and hyperbolic initial-boundary value problems when a combination of the values of the solution initially and at a later time is prescribed. 相似文献
12.
A priori bounds for semilinear equations and a new class of critical exponents for Lipschitz domains
P.J. McKenna 《Journal of Functional Analysis》2007,244(1):220-246
A priori bounds for positive, very weak solutions of semilinear elliptic boundary value problems −Δu=f(x,u) on a bounded domain Ω⊂Rn with u=0 on ∂Ω are studied, where the nonlinearity 0?f(x,s) grows at most like sp. If Ω is a Lipschitz domain we exhibit two exponents p* and p*, which depend on the boundary behavior of the Green function and on the smallest interior opening angle of ∂Ω. We prove that for 1<p<p* all positive very weak solutions are a priori bounded in L∞. For p>p* we construct a nonlinearity f(x,s)=a(x)sp together with a positive very weak solution which does not belong to L∞. Finally we exhibit a class of domains for which p*=p*. For such domains we have found a true critical exponent for very weak solutions. In the case of smooth domains is an exponent which is well known from classical work of Brezis, Turner [H. Brezis, R.E.L. Turner, On a class of superlinear elliptic problems, Comm. Partial Differential Equations 2 (1977) 601-614] and from recent work of Quittner, Souplet [P. Quittner, Ph. Souplet, A priori estimates and existence for elliptic systems via bootstrap in weighted Lebesgue spaces, Arch. Ration. Mech. Anal. 174 (2004) 49-81]. 相似文献
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F. Rendl 《European Journal of Operational Research》1985,20(3):363-372
The eigenvalue bound for the quadratic assignment problem (QAP) is successively improved by considering a set of k-best scalar products, related to the QAP. An efficient procedure is proposedto find such a set of k-best scalar products. A class of QAPs is described for which this procedure in general improves existing lower bounds and at the same time generates good suboptimal solutions. The method leaves the user with a large flexibility in controlling the quality of the bound. However, since the method is sensitive to input data it should only be used in combination with other bounding rules. 相似文献
15.
Rodrigo Meneses 《Journal of Mathematical Analysis and Applications》2011,376(2):514-527
In this paper, we prove that a class of parabolic equations involving a second order fully nonlinear uniformly elliptic operator has a Fujita type exponent. These exponents are related with an eigenvalue problem in all RN and play the same role in blow-up theorems as the classical p?=1+2/N introduced by Fujita for the Laplacian. We also obtain some associated existence results. 相似文献
16.
We study whether the solutions of a fully nonlinear, uniformly parabolic equation with superquadratic growth in the gradient satisfy initial and homogeneous boundary conditions in the classical sense, a problem we refer to as the classical Dirichlet problem. Our main results are: the nonexistence of global-in-time solutions of this problem, depending on a specific largeness condition on the initial data, and the existence of local-in-time solutions for initial data up to the boundary. Global existence is know when boundary conditions are understood in the viscosity sense, what is known as the generalized Dirichlet problem. Therefore, our result implies loss of boundary conditions in finite time. Specifically, a solution satisfying homogeneous boundary conditions in the viscosity sense eventually becomes strictly positive at some point of the boundary. 相似文献
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Philippe Souplet 《Annali di Matematica Pura ed Applicata》2002,181(4):427-436
We prove an a priori estimate and a universal bound for any global solution of the nonlinear degenerate reaction-diffusion
equation u
t
=Δu
m
+u
p
in a bounded domain with zero Dirichlet boundary conditions.
Received: October 1, 2001?Published online: July 9, 2002 相似文献
20.
Marcelo Montenegro 《Journal of Functional Analysis》2010,259(2):428-452
We establish Lipschitz regularity for solutions to a family of non-isotropic fully nonlinear partial differential equations of elliptic type. In general such a regularity is optimal. No sign constraint is imposed on the solution, thus limiting free boundaries may have two-phases. Our estimates are then employed in combination with fine regularizing techniques to prove existence of viscosity solutions to singular nonlinear PDEs. 相似文献