共查询到20条相似文献,搜索用时 15 毫秒
1.
C. A. Stuart 《Milan Journal of Mathematics》2011,79(1):327-341
For a class of second order quasilinear elliptic equations we establish the existence of two non–negative weak solutions of
the Dirichlet problem on a bounded domain, Ω. Solutions of the boundary value problem are critical points of C
1–functional on H01(W){H_0^1(\Omega)}. One solution is a local minimum and the other is of mountain pass type. 相似文献
2.
D. V. Portnyagin 《Ukrainian Mathematical Journal》2006,58(8):1223-1237
The L
∞-estimates of weak solutions are established for a quasilinear nondiagonal parabolic system of singular equations whose matrix
of coefficients satisfies special structural conditions. A procedure based on the estimation of linear combinations of the
unknowns is used.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 8, pp. 1084–1096, August, 2006. 相似文献
3.
Nicola Garofalo 《manuscripta mathematica》2009,130(3):375-385
In a Carnot group we prove a new priori bound for the right-invariant horizontal gradient of smooth solutions of a class of
quasilinear equations which are modeled on the so-called horizontal p-Laplacian. Exploiting such bound and a regularization procedure based on difference quotients we obtain the C1,aloc{C^{1,\alpha}_{loc}} regularity of weak solutions which possess some special symmetries. For instance, in the first Heisenberg group
\mathbbH1{\mathbb{H}^{1}} we obtain such regularity for all weak solutions of the horizontal p-Laplacian, with p ≥ 2, which are of the form u(z, t) = u(|z|, t). 相似文献
4.
We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence
form under natural growth conditions. The degeneracy is given by a suitable power of a strong A
∞ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove C
1,α
local estimates for solutions of a degenerate equation in non divergence form. 相似文献
5.
Solution of the spectral problem for the curl and Stokes operators with periodic boundary conditions
R. S. Saks 《Journal of Mathematical Sciences》2006,136(2):3794-3811
In this paper, we establish relations between eigenvalues and eigenfunctions of the curl operator and Stokes operator (with
periodic boundary conditions). These relations show that the curl operator is the square root of the Stokes operator with
ν = 1. The multiplicity of the zero eigenvalue of the curl operator is infinite. The space L
2(Q, 2π) is decomposed into a direct sum of eigenspaces of the operator curl. For any complex number λ, the equation rot
u + λu = f and the Stokes equation −ν(Δv + λ 2v) + ∇p = f, div v = 0, are solved. Bibliography: 15 titles.
Dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 246–276. 相似文献
6.
Qi-kang Ran Ai-nong FangDepartment of Applied Mathematics Shanghai University of Finance Economics Shanghai ChinaDepartment of Applied Mathematics Shanghai Jiaotong University Shanghai China 《应用数学学报(英文版)》2002,18(3):461-470
In this paper, using capacity theory and extension theorem of Lipschitz functions we first discuss the uniqueness of weak solution of nonhomogeneous quasilinear elliptic equationsin space W(θ,p)(Ω), which is bigger than W1,p(Ω). Next, using revise reverse Holder inequality we prove that if ωc is uniformly p-think, then there exists a neighborhood U of p, such that for all t ∈U, the weak solutions of equation corresponding t are bounded uniformly. Finally, we get the stability of weak solutions on exponent p. 相似文献
7.
Jia-cheng Lan 《应用数学学报(英文版)》2005,21(4):615-622
In this paper, the author discusses the multilinear singular integrals with certain θ-type Calderdn- Zygmund operators and obtain the boundedness from weak H^1 (R^n) to weak L^1 (R^n). 相似文献
8.
We analyze a class of quasilinear elliptic problems involving a p(·)-Laplace-type operator on a bounded domain
W ì \mathbb RN{\Omega\subset{\mathbb R}^N}, N ≥ 2, and we deal with nonlinear conditions on the boundary. Working on the variable exponent Lebesgue–Sobolev spaces, we
follow the steps described by the “fountain theorem” and we establish the existence of a sequence of weak solutions. 相似文献
9.
Based on a comparison principle, we discuss the existence, uniqueness and asymptotic behaviour of various boundary blow-up
solutions, for a class of quasilinear elliptic equations, which are then used to obtain a rather complete understanding of
some quasilinear elliptic problems on a bounded domain or over the entireR
N
. 相似文献
10.
Bernhard Hein 《Calculus of Variations and Partial Differential Equations》2007,28(2):249-273
In
, n < 7, we treat the quasilinear, degenerate parabolic initial and boundary value problem which is the natural parabolic extension of Huisken and Ilmanen’s weak inverse mean curvature flow (IMCF). We prove long time existence and partial uniqueness of Lipschitz continuous weak solutions u(x,t) and show C
1,α-regularity for the sets ∂{x| u(x,t) < z }. Our approach offers a new approximation for weak solutions of the IMCF starting from a class of interesting and easily obtainable initial values; for these, the above sets are shown to converge against corresponding surfaces of the IMCF as t → ∞ globally in Hausdorff distance and locally uniformly with respect to the C
1,α-norm.Research partially supported by the DFG, SFB 382 at Tübingen University 相似文献
11.
Let D??3 be a bounded domain with connected boundary δD of class C2. It is shown that Herglotz wave functions are dense in the space of solutions to the Helmholtz equation with respect to the norm in H1(D) and that the electric fields of electromagnetic Herglotz pairs are dense in the space of solutions to curl curl E=k2E with respect to the norm in Hcurl(D). Two proofs are given in each case, one based on the denseness of the traces of Herglotz wave functions on δD and the other on variational methods. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
12.
Hongjun YUAN 《数学年刊B辑(英文版)》2007,28(4):475-498
The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form U_t-Δφ(u)=O, whereφ■C~1(R~1)is a strictly monotone increasing function.Clearly,the above equation has strong degeneracy,i.e.,the set of zero points ofφ′(·)is permitted to have zero measure. This is an answer to an open problem in[13,p.288]. 相似文献
13.
We study a class of quasilinear elliptic equations on the unit ball of ℝ
n
in the divergence form ∑
j=1
n
D
j{G(|x|2,|Du|2)D
j
u} =H(|x|) and get estimates on the boundary by using a modified barrier-function technique of Bernstein. We establish a maximum principle
for the gradients of solutions and get a global gradient estimate. We prove that solutions with constant boundary condition
must be radial. Finally, we apply these results to graphs {(x,u(x)):x∈H
n
} whereu:H
n
→ℝ is a smooth map of then-hyperbolic spaceH
n
=B(0,1) with the metric
to get the existence of graphs with radial prescribed mean curvature. 相似文献
14.
15.
On partial regularity of suitable weak solutions to the Navier–Stokes equations in unbounded domains
Tomoyuki Suzuki 《manuscripta mathematica》2008,125(4):471-493
Consider the nonstationary Navier–Stokes equations in Ω × (0, T), where Ω is a general unbounded domain with non-compact boundary in R
3. We prove the regularity of suitable weak solutions for large |x|. It should be noted that our result also holds near the boundary. Our result extends the previous ones by Caffarelli–Kohn–Nirenberg
in R
3 and Sohr-von Wahl in exterior domains to general domains. 相似文献
16.
Takahiro Okabe 《Journal of Evolution Equations》2011,11(2):265-286
We consider the initial boundary value problem to the Navier–Stokes equations in a bounded domain with the inhomogeneous time-dependent
data b(t) ? H1/2(?W){\beta(t) \in H^{1/2}(\partial\Omega)} under the general flux condition. We establish a reproductive property for weak solutions of the Navier–Stokes equations.
Here, the reproductive property is regarded as the generalization of the time periodicity. As an application, we can prove
the existence of periodic weak solutions. 相似文献
17.
Global bifurcation of positive solutions for some degenerate quasilinear elliptic problems is considered. The uniform estimate
of the gradient of weak solutions is given. This estimate is crucial in our arguments.
Received: 10 August 2001
Supported in part by Grant-in-Aid for Scientific Research (No. 11640207), Ministry of Education, Science, Sports and Culture,
Japan.
Mathematics Subject Classification (2000): 35B32, 35J25, 35J70 相似文献
18.
By introducing the concept of the weak linear degeneracy the authors give a complete result for the global existence and for the life span of C1 solutions to the Cauchy problem for general first order quasilinear hyperbolic systems with initial data small in C1 norm and with compact support. 相似文献
19.
A class of strongly coupled parabolic systems, modeling the energy transport of electrons in semiconductors, is analyzed.
The variables are the electron density and the thermal energy. First, some Lyapunov functionals are derived, which yields
the weak sequential stability for smooth solutions in the sense of Feireisl, using weak compactness results. Second, by the
H
−1 method, the uniqueness of bounded weak solutions is proved. 相似文献
20.
Albert Milani 《Mathematische Nachrichten》1999,199(1):115-144
We prove that C2+α,1+α/2 (Q?) solutions of problem (1.6) below are in a subspace Hcm+2(Q) of Hm+2,(m+2)/2(Q) for all m ∈ ?, if f and the coefficients are in Hcm(Q)∪Cα,α/2 (Q?). We apply this result to obtain global existence of Sobolev solutions to the quasilinear problem (1.26) below. 相似文献