共查询到20条相似文献,搜索用时 31 毫秒
1.
Kaouther Ammar 《Journal of Differential Equations》2007,234(1):1-25
We consider a general class of degenerate elliptic problems of the form Au+g(x,u,Du)=f, where A is a Leray-Lions operator from a weighted Sobolev space into its dual. We assume that g(x,s,ξ) is a Caratheodory function verifying a sign condition and a growth condition on ξ. Existence of renormalized solutions is established in the L1-setting. 相似文献
2.
Lech Zarȩba 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(4):445-467
In this paper we consider the mixed problem for the equation u
tt
+ A
1
u + A
2(u
t
) + g(u
t
) = f(x, t) in unbounded domain, where A
1 is a linear elliptic operator of the fourth order and A
2 is a nonlinear elliptic operator of the second order. Under natural assumptions on the equation coefficients and f we proof existence of a solution. This result contains, as a special case, some of known before theorems of existence. Essentially,
in difference up to previous results we prove theorems of existence without the additional assumption on behavior of solution
at infinity.
相似文献
3.
Olivier Guibé 《Annali di Matematica Pura ed Applicata》2002,180(4):441-449
We give a partial uniqueness result concerning comparable renormalized solutions of the nonlinear elliptic problem -div(a(x,Du))=μ in Ω, u=0 on ∂Ω, where μ is a Radon measure with bounded variation on Ω.
Received: December 27, 2000 Published online: December 19, 2001 相似文献
4.
We consider a solution u of the homogeneous Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) + g(x, u) = f, where the principal term is a Leray–Lions operator defined on and g(x, u) is a term having the same sign as u and satisfying suitable growth assumptions. We prove that the rearrangement of u can be estimated by the solution of a problem whose data are radially symmetric. 相似文献
5.
We study the multi-channel Gel?fand–Calderón inverse problem in two dimensions, i.e. the inverse boundary value problem for the equation −Δψ+v(x)ψ=0, x∈D, where v is a smooth matrix-valued potential defined on a bounded planar domain D. We give an exact global reconstruction method for finding v from the associated Dirichlet-to-Neumann operator. This also yields a global uniqueness results: if two smooth matrix-valued potentials defined on a bounded planar domain have the same Dirichlet-to-Neumann operator then they coincide. 相似文献
6.
A basic integral equation of random fields estimation theory by the criterion of minimum of variance of the estimation error is of the form Rh = f, where
and R(x, y) is a covariance function.The singular perturbation problem we study consists of finding the asymptotic behavior of the solution to the equation
as
0.$$" align="middle" border="0">
The domain D can be an interval or a domain in Rn, n > 1. The class of operators R is defined by the class of their kernels R(x,y) which solve the equation Q(x, Dx)R(x, y) = P(x, Dx)δ(x − y), where Q(x, Dx) and Px, Dx) are elliptic differential operators. 相似文献
7.
In the present article we are concerned with a class of degenerate second order differential operators LA,b defined on the cube d[0,1], with d?1. Under suitable assumptions on the coefficients A and b (among them the assumption of their Hölder regularity) we show that the operator LA,b defined on C2(d[0,1]) is closable and its closure is m-dissipative. In particular, its closure is the generator of a C0-semigroup of contractions on C(d[0,1]) and C2(d[0,1]) is a core for it. The proof of such result is obtained by studying the solvability in Hölder spaces of functions of the elliptic problem λu(x)−LA,bu(x)=f(x), x∈d[0,1], for a sufficiently large class of functions f. 相似文献
8.
We consider the divergence form elliptic operator A=??x,z·(c2(x,z) ?x,z) in the strip Ω=?× [0,H]. The velocity c(x,z) describes the multistratification of Ω: a horizontal stratification with a compact perturbation K, the velocity in K is a L∞(K) function. We suppose that the position of the perturbation is known and we prove uniqueness for identification of the perturbation from one generalized eigenfunction pattern in the neighbourhood of K. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
9.
Hyun Jae Yoo 《Mathematische Zeitschrift》2006,252(1):27-48
We consider fermion (or determinantal) random point fields on Euclidean space ℝd. Given a bounded, translation invariant, and positive definite integral operator J on L2(ℝd), we introduce a determinantal interaction for a system of particles moving on ℝd as follows: the n points located at x1,· · ·,xn ∈ ℝd have the potential energy given by where j(x−y) is the integral kernel function of the operator J. We show that the Gibbsian specification for this interaction is well-defined. When J is of finite range in addition, and for d≥2 if the intensity is small enough, we show that the fermion random point field corresponding to the operator J(I+J)−1 is a Gibbs measure admitted to the specification. 相似文献
10.
We study uniformly elliptic fully nonlinear equations of the type F(D2u,Du,u,x)=f(x). We show that convex positively 1-homogeneous operators possess two principal eigenvalues and eigenfunctions, and study these objects; we obtain existence and uniqueness results for nonproper operators whose principal eigenvalues (in some cases, only one of them) are positive; finally, we obtain an existence result for nonproper Isaac's equations. 相似文献
11.
We consider the Dirichlet problem for a class of quasilinear degenerate elliptic inclusions of the form ?div(𝒜(x, u, ?u)) + f(x)g(u) ∈ H(x, u, ?u), where 𝒜(x, u, ?u) is allowed to be degenerate. Without the general assumption that the multivalued nonlinearity is characterized by Clarke's generalized gradient of some locally Lipschitz functions, we prove the existence of bounded solutions in weighed Sobolev space with the superlinear growth imposed on the nonlinearity g and the multifunction H(x, u, ?u) by using the Leray-Schauder fixed point theorem. Furthermore, we investigate the existence of extremal solutions and prove that they are dense in the solutions of the original system. Subsequently, a quasilinear degenerate elliptic control problem is considered and the existence theorem based on the proven results is obtained. 相似文献
12.
13.
Alexander Kovalevsky 《Applicable analysis》2013,92(10):1207-1217
We consider a class of degenerate nonlinear elliptic fourth-order equations in divergence form. Coefficients of the equations satisfy a strengthened ellipticity condition involving two weighted functions. The right-hand side F?(x,?u) of the equations depends on the unknown function u. Under some conditions, including Lm -summability of F(·, 0) with m close to 1 and restrictions on the exponent σ of the growth of F?(x,?u) with respect to u, we establish existence of W-solutions of the Dirichlet problem for the given equations and describe the dependence of summability properties of these solutions on m and σ. 相似文献
14.
Erhard Heinz Ralf Beyerstedt 《Calculus of Variations and Partial Differential Equations》1994,2(2):241-247
Letz=z(x, y) be a real-valued twice continuously differentiable solution of the elliptic Monge-Ampère equationAr+2Bs+Ct+rt – s
2=E in the punctured disk 0<(x–x
0)2+(y–y
0)2<2. Assume thatq is continuous at (x0, y0). Our aim is to give sufficient conditions on the coefficientsA,..., E which ensure that the singularity (x
0,y
0) is removable. This generalizes an earlier result of Jörgens (Math. Ann. 129 (1955), 330–344). 相似文献
15.
Kyungkeun Kang 《Journal of Differential Equations》2011,251(9):2466-2493
We study the 3×3 elliptic systems ∇(a(x)∇×u)−∇(b(x)∇⋅u)=f, where the coefficients a(x) and b(x) are positive scalar functions that are measurable and bounded away from zero and infinity. We prove that weak solutions of the above system are Hölder continuous under some minimal conditions on the inhomogeneous term f. We also present some applications and discuss several related topics including estimates of the Green?s functions and the heat kernels of the above systems. 相似文献
16.
Louis Dupaigne 《Journal de Mathématiques Pures et Appliquées》2007,87(6):563-581
We are concerned with singular elliptic problems of the form −Δu±p(d(x))g(u)=λf(x,u)+μa|∇u| in Ω, where Ω is a smooth bounded domain in RN, d(x)=dist(x,∂Ω), λ>0, μ∈R, 0<a?2, and f is a nondecreasing function. We assume that p(d(x)) is a positive weight with possible singular behavior on the boundary of Ω and that the nonlinearity g is unbounded around the origin. Taking into account the competition between the anisotropic potential p(d(x)), the convection term a|∇u|, and the singular nonlinearity g, we establish various existence and nonexistence results. 相似文献
17.
Houman Owhadi 《Probability Theory and Related Fields》2003,125(2):225-258
This paper is concerned with the approximation of the effective conductivity σ(A, μ) associated to an elliptic operator ∇
xA
(x,η)∇
x
where for xℝ
d
, d≥1, A(x,η) is a bounded elliptic random symmetric d×d matrix and η takes value in an ergodic probability space (X, μ). Writing A
N
(x, η) the periodization of A(x, η) on the torus T
d
N
of dimension d and side N we prove that for μ-almost all η
We extend this result to non-symmetric operators ∇
x
(a+E(x, η))∇
x
corresponding to diffusions in ergodic divergence free flows (a is d×d elliptic symmetric matrix and E(x, η) an ergodic skew-symmetric matrix); and to discrete operators corresponding to random walks on ℤ
d
with ergodic jump rates.
The core of our result is to show that the ergodic Weyl decomposition associated to 2(X, μ) can almost surely be approximated by periodic Weyl decompositions with increasing periods, implying that semi-continuous
variational formulae associated to 2(X, μ) can almost surely be approximated by variational formulae minimizing on periodic potential and solenoidal functions.
Received: 10 January 2002 / Revised version: 12 August 2002 / Published online: 14 November 2002
Mathematics Subject Classification (2000): Primary 74Q20, 37A15; Secondary 37A25
Key words or phrases: Effective conductivity – periodization of ergodic media – Weyl decomposition 相似文献
18.
Helmut Abels 《偏微分方程通讯》2013,38(10):1463-1503
ABSTRACT In this contribution, we establish a calculus of pseudodifferential boundary value problems with Hölder continuous coefficients. It is a generalization of the calculus of pseudodifferential boundary value problems introduced by Boutet de Monvel. We discuss their mapping properties in Bessel potential and certain Besov spaces. Although having non-smooth coefficients and the operator classes being not closed under composition, we will prove that the composition of Green operators a 1(x, D x )a 2(x, D x ) coincides with a Green operator a(x, D x ) up to order m 1 + m 2 ? Θ, where Θ ∈ (0, τ2) is arbitrary, a j (x, ξ) is in C τ j (? n ) w.r.t. x, and m j is the order of a j (x, D x ), j = 1, 2. Moreover, a(x, D x ) is obtained by the asymptotic expansion formula of the smooth coefficient case leaving out all terms of order less than m 1 + m 2 ? Θ. This result is used to construct a parametrix of a uniformly elliptic Green operator a(x, D x ). 相似文献
19.
We consider the elliptic operator Lu(x):= xu″(x)+β(x)u′(x) + γ (x)u(x) with Wentzell-type boundary condition, in spaces of continuous function on [0,+∞[. We prove that such operators generate
positive C
0-semigroup which can be approximated by means of iterated of modified Szász-Mirakjan operators here introduced. 相似文献
20.
Reika Fukuizumi Tohru Ozawa 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(6):1000-1011
Exponential decay estimates are obtained for complex-valued solutions to nonlinear elliptic equations in
where the linear term is given by Schr?dinger operators H = − Δ + V with nonnegative potentials V and the nonlinear term is given by a single power with subcritical Sobolev exponent in the attractive case. We describe specific
rates of decay in terms of V, some of which are shown to be optimal. Moreover, our estimates provide a unified understanding of two distinct cases in
the available literature, namely, the vanishing potential case V = 0 and the harmonic potential case V(x) = |x|2.
Dedicated to Professor Jun Uchiyama on the occasion of his sixtieth birthday
Received: May 4, 2004 相似文献