共查询到20条相似文献,搜索用时 234 毫秒
1.
Lawrence C. Evans Ovidiu Savin 《Calculus of Variations and Partial Differential Equations》2008,32(3):325-347
We propose a new method for showing C
1, α
regularity for solutions of the infinity Laplacian equation and provide full details of the proof in two dimensions. The
proof for dimensions n ≥ 3 depends upon some conjectured local gradient estimates for solutions of certain transformed PDE.
LCE is supported in part by NSF Grant DMS-0500452. OS was supported in part by the Miller Institute for Basic Research in
Science, Berkeley. 相似文献
2.
Haïm Brezis Jean Van Schaftingen 《Calculus of Variations and Partial Differential Equations》2007,30(3):369-388
We obtain boundary estimates for the gradient of solutions to elliptic systems with Dirichlet or Neumann boundary conditions
and L
1–data, under some condition on the divergence of the data. Similar boundary estimates are obtained for div–curl and Hodge
systems. 相似文献
3.
4.
Sun-Sig Byun 《Journal of Evolution Equations》2007,7(3):415-428
This work treats Lp regularity theory for weak solutions of parabolic equations in divergence form with discontinuous coefficients on nonsmooth
domains. We essentially obtain an optimal condition on the coefficients under which the global W1,p regularity theory holds.
This work was supported by SNU foundation in 2005. 相似文献
5.
José Francisco Rodrigues Manel Sanchón José Miguel Urbano 《Monatshefte für Mathematik》2008,154(4):303-322
The aim of this paper is twofold: to prove, for L
1-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable
growth, and to show some convergence and stability properties of the corresponding coincidence set. The latter follow from
extending the Lewy-Stampacchia inequalities to the general framework of L
1.
Current address: Manel Sanchón, Universitat de Barcelona, Departament de Matemàtica Aplicada i Anàlisi, Gran Via 585, 08007
Barcelona, Spain; e-mail: msanchon@maia.ub.es
Authors’ addresses: J. F. Rodrigues, CMUC, Department of Mathematics, University of Coimbra, and FCUL/Universidade de Lisboa,
Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal; M. Sanchón and J. M. Urbano, CMUC, Department of Mathematics, University
of Coimbra, 3001-454 Coimbra, Portugal 相似文献
6.
We study the Cauchy problem for time-dependent diffusion operators with singular coefficients on L1-spaces induced by infinitesimal invariant measures. We give sufficient conditions on the coefficients such that the Cauchy-Problem is well-posed. We construct associated diffusion processes with the help of the theory of generalized Dirichlet forms. We apply our results in particular to construct a large class of Nelson-diffusions that could not been constructed before. 相似文献
7.
We introduce the concept of Lp-maximal regularity for second order Cauchy problems. We prove Lp-maximal regularity for an abstract model problem and we apply the abstract results to prove existence, uniqueness and regularity
of solutions for nonlinear wave equations.
The author acknowledges with thanks the support provided by the Department ofApplied Analysis, University of Ulm, and the
travel grants provided by NBMH India and MSF Delhi, India. 相似文献
8.
We study Lp-viscosity solutions of fully nonlinear, second-order, uniformly elliptic partial differential equations (PDE) with measurable terms and quadratic nonlinearity. We present a sufficient condition under which the maximum principle holds for Lp-viscosity solution. We also prove stability and existence results for the equations under consideration. 相似文献
9.
In this paper we prove Lp estimates (p≥2) for the uniform norm of the paths of solutions of quasilinear stochastic partial differential equations (SPDE) of parabolic
type. Our method is based on a version of Moser's iteration scheme developed by Aronson and Serrin in the context of non-linear
parabolic PDE. 相似文献
10.
We consider the problem of prescribing scalar curvature on the standard 2-sphere S
2. It is proved that any positive smooth function on S
2 is the scalar curvature of some pointwise conformal metric, if an associated map has non-zero degree. As a result we improve some previous important results and give some completely new ones.Received: 21 January 2003, Accepted: 12 March 2003, Published online: 6 June 2003Mathematics Subject Classification (2000):
35J60, 58G03Min Ji: Supported in part by the NSF grant 19725102 and the 973 grant G1999075107 of China 相似文献
11.
A new approximation technique based on L
1-minimization is introduced. It is proven that the approximate solution converges to the viscosity solution in the case of
one-dimensional stationary Hamilton–Jacobi equation with convex Hamiltonian.
This material is based upon work supported by the National Science Foundation grant DMS-0510650.
J.-L. Guermond is on leave from LIMSI, UPRR 3251 CNRS, BP 133, 91403 Orsay Cedex, France. 相似文献
12.
Countably generated prime ideals in <Emphasis Type="Italic">H</Emphasis><Superscript>∞</Superscript>
We confirm a twenty year old conjecture by showing that a nonzero prime ideal P in the algebra H∞ of bounded analytic functions in the open unit disk is countably generated if and only if it is either a principal ideal
generated by the polynomial z−z0, |z0|<1, or if P is generated by the n-th roots of an atomic inner function. The case of the algebra H∞+C is also dealt with.
Dedicated to the 70th birthday of Joseph Cima
Research supported by the RIP-program Oberwolfach 2004. 相似文献
13.
The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator:
is considered, where Θ is a bounded domain in R
n
(n>p>1) with smooth boundary ∂Θ. Under some natural conditions together with some conditions weaker than (AR) condition, we prove that the above problem
has infinitely many solutions by a symmetric version of the Mountain Pass Theorem if
.
Supported by the National Natural Science Foundation of China (10171032) and the Guangdong Provincial Natural Science Foundation
(011606). 相似文献
14.
In this paper the optimal L
2 error estimates of the finite volume element methods (FVEM) for Poisson equation are discussed on quadrilateral meshes. The
trial function space is taken as isoparametric bilinear finite element space on quadrilateral partition, and the test function
space is defined as piecewise constant space on dual partition. Under the assumption that all elements on quadrilateral meshes
are O(h
2) quasi-parallel quadrilateral elements, we prove convergence rate to be O(h
2) in L
2 norm. 相似文献
15.
Bao Qin Li 《Mathematische Zeitschrift》2008,258(4):763-771
We show that meromorphic solutions f, g of f
2 + g
2 = 1 in C2 must be constant, if f
z2 and g
z1 have the same zeros (counting multiplicities). We also apply the result to characterize meromorphic solutions of certain
nonlinear partial differential equations. 相似文献
16.
We consider the mixed problem,
in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. We suppose the Dirichlet data,
f
D
, has one derivative in L
p
(D) of the boundary and the Neumann data, f
N
, is in L
p
(N). We find a p
0 > 1 so that for p in an interval (1, p
0), we may find a unique solution to the mixed problem and the gradient of the solution lies in L
p
.
L. Lanzani, L. Capogna and R. M. Brown were supported, in part, by the U.S. National Science Foundation. 相似文献
17.
Elena V. Vernigora 《Journal of Mathematical Sciences》2012,182(1):108-116
We consider the construction of of an inversive congruential generator over a Galois ring of odd dimension p
l
, whichwas proposed by Solé and Zinoviev for p = 2. Using the estimates of trigonometric sums on the sequences of pseudorandom numbers, we obtain the estimates of a discrepant
function, a generated sequence of pseudorandom numbers, and the associated sequence of two-dimensional “overlapping” points. 相似文献
18.
Xavier Cabré Antonio Capella Manel Sanchón 《Calculus of Variations and Partial Differential Equations》2009,34(4):475-494
We consider semi-stable, radially symmetric, and decreasing solutions of − Δ
p
u = g(u) in the unit ball of , where p > 1, Δ
p
is the p-Laplace operator, and g is a locally Lipschitz function. For this class of radial solutions, which includes local minimizers, we establish pointwise,
L
q
, and W
1,q
estimates which are optimal and do not depend on the specific nonlinearity g. Among other results, we prove that every radially decreasing and semi-stable solution u belonging to W
1,p
(B
1) is bounded whenever n < p + 4p/(p − 1). Under standard assumptions on the nonlinearity g(u) = λf (u), where λ > 0 is a parameter, it is proved that the corresponding extremal solution u
* is semi-stable, and hence, it enjoys the regularity stated in our main result. 相似文献
19.
ZhangJianfeng 《高校应用数学学报(英文版)》2005,20(2):183-196
Let M^n be a closed spacelike submanifold isometrically immersed in de Sitter space Sp^(n p)(c), Denote by R,H and S the normalized scalar curvature,the mean curvature and the square of the length of the second fundamental form of M^n ,respectively. Suppose R is constant and R≤c. The pinching problem on S is studied and a rigidity theorem for M^n immersed in Sp^(n p)(c) with parallel normalized mean curvature vector field is proved. When n≥3, the pinching constant is the best. Thus, the mistake of the paper “Space-like hypersurfaces in de Sitter space with constant scalar curvature”(see Manus Math, 1998,95 :499-505) is corrected. Moreover,the reduction of the codimension when M^n is a complete submanifold in Sp^(n p)(c) with parallel normalized mean curvature vector field is investigated. 相似文献
20.
Qiuyi Dai Yonggeng Gu Jiuyi Zhu 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7126-7136
This paper concerns a priori estimates and existence of solutions of generalized mean curvature equations with Dirichlet boundary value conditions in smooth domains. Using the blow-up method with the Liouville-type theorem of the p laplacian equation, we obtain a priori bounds and the estimates of interior gradient for all solutions. The existence of positive solutions is derived by the topological method. We also consider the non-existence of solutions by Pohozaev identities. 相似文献