共查询到20条相似文献,搜索用时 250 毫秒
1.
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
2.
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
3.
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
4.
We obtain a priori estimates for solutions to the prescribed scalar curvature equation on S
3. The usual non-degeneracy assumption on the curvature function is replaced by a new condition, which is necessary and sufficient
for the existence of a priori estimates, when the curvature function is a positive Morse function. 相似文献
5.
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
6.
Michael J. Puls 《Archiv der Mathematik》2007,88(6):500-506
Let p be a real number greater than one. In this paper we study the vanishing and nonvanishing of the first L
p
-cohomology space of some groups that have one end. We also make a connection between the first L
p
-cohomolgy space and the Floyd boundary of the Cayley graph of a group. We apply the result about Floyd boundaries to show
that there exists a real number p such that the first L
p
-cohomology space of a nonelementary hyperbolic group does not vanish.
Received: 4 August 2006 Revised: 2 November 2006 相似文献
7.
8.
The C
*-algebra
generated by the n poly-Bergman and m antipoly-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space
L
2(Π) over the upper half-plane is studied. Making use of a local principle, limit operators techniques, and the Plamenevsky
results on two-dimensional convolution operators with symbols admitting homogeneous discontinuities we reduce the study to
simpler C
*-algebras associated with points
and pairs
. Applying a symbol calculus for the abstract unital C
*-algebras generated by N orthogonal projections sum of which equals the unit and by M = n + m one-dimensional orthogonal projections and using relations for the Gauss hypergeometric function, we study local algebras
at points
being the discontinuity points of coefficients. A symbol calculus for the C
*-algebra
is constructed and a Fredholm criterion for the operators
is obtained. 相似文献
9.
We investigate R-bounded representations
, where X is a Banach space and G is a lca group. Observing that Ψ induces a (strongly continuous) group homomorphism
, we are then able to analyze certain classical homomorphisms U (e.g. translations in Lp (G)) from the viewpoint of R-boundedness and the theory of scalar-type spectral operators.
Dedicated to the memory of H. H. Schaefer 相似文献
10.
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
11.
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
12.
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
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.
José E. Galé Pedro J. Miana Detlef Müller 《Integral Equations and Operator Theory》2007,57(3):327-337
We consider some extensions of well-boundedness and Cm-scalarity by using fractional calculus, and prove some theorems accordingly. These results are applied to the usual Laplacian
on Rn and sub-Laplacians on nilpotent Lie groups.
The research of first and second authors has been partly supported by the Project MTM2004-03036 of the M.C.YT.-DGI/F.E.D.E.R.,
Spain, and the Project E-12/25, D. G. Aragón, Spain. Part of the research of second author was developed in the Christian-Albrechts
Universit?t in Kiel, while he was enjoying a HARP-postdoctoral position in the European Harmonic Analysis Network, HARP, IHP
2002-06. 相似文献
15.
We study existence and a priori estimates of invariant measures μ for SPDE with local Lipschitz drift coefficients. Furthermore, we discuss the corresponding parabolic Cauchy-problem in L
1(μ). Particular emphasis will be put on stochastic reaction diffusion equations.
相似文献
16.
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
17.
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
18.
Let X be a Banach space and let
A be a closed linear operator on
X. It is shown that the abstract Cauchy problem
enjoys maximal regularity in weighted
L
p
-spaces with weights
, where
,
if and only if it has the property of maximal
L
p
-regularity.
Moreover, it is also shown that the derivation operator
admits an
-calculus in weighted
L
p
-spaces.
Received: 26 February 2003 相似文献
19.
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
20.
Michael T. Jury 《Integral Equations and Operator Theory》2007,58(3):341-362
We analyze the essential sectrum and index theory of elements of Toeplitz-composition C*-algebras (algebras generated by the Toeplitz algebra and a single linear-fractional composition operator, acting on the Hardy
space of the unit disk). For automorphic composition operators we show that the quotient of the Toeplitz-composition algebra
by the compacts is isomorphic to the crossed product C*-algebra for the action of the symbol on the boundary circle. Using this result we obtain sufficient conditions for polynomial
elements of the algebra to be Fredholm, by analyzing the spectrum of elements of the crossed product. We also obtain an integral
formula for the Fredholm index in terms of a generalized Chern character. Finally we prove an index formula for the case of
the non-parabolic, non-automorphic linear fractional maps studied by Kriete, MacCluer and Moorhouse. 相似文献