共查询到20条相似文献,搜索用时 15 毫秒
1.
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
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.
4.
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
5.
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
6.
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
7.
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
8.
We study the L-series of cubic fourfolds. Our main result is that, if X/C is a special cubic fourfold associated to some polarized K3 surface S, defined over a number field K and satisfying , then X has a model over K such that the L-series of the primitive cohomology of X/K can be expressed in terms of the L-series of S/K. This allows us to compute the L-series for a discrete dense subset of cubic fourfolds in the moduli spaces of certain special cubic fourfolds. We also discuss
a concrete example. 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.
A weighted norm inequality for the Marcinkiewicz integral operator
is proved when belongs to
. We also give the weighted
Lp-boundedness for a class of Marcinkiewicz integral operators with rough
kernels
and
related to the Littlewood-Paley
-function and the
area integral S, respectively. 相似文献
11.
12.
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
13.
We show that any pointwise multiplier for BMO(ℝn) generates a function p from the class (ℝn) of those functions for which the Hardy-Littlewood maximal operator is bounded on the variable Lp space. In particular, this gives a positive answer to Diening's conjecture saying that there are discontinuous functions
which nevertheless belong to (ℝn). 相似文献
14.
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
15.
Anders Edquist Erik Lindgren 《Calculus of Variations and Partial Differential Equations》2009,35(4):421-433
We study the so-called two-phase obstacle-type problem for the p-Laplacian when p is close to 2. We introduce a new method to obtain the optimal growth of the function from branch points, i.e. two-phase
points in the free boundary where the gradient vanishes. As a by-product we can locally estimate the (n − 1)-Hausdorff-measure of the free boundary for the special case when p > 2.
This research project is a part of the ESF program Global. E. Lindgren has been supported by grant KAW 2005.0098 from the
Knut and Alice Wallenberg foundation. 相似文献
16.
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
17.
Robert J. Taggart 《Mathematische Zeitschrift》2009,261(4):933-949
Suppose that {T
t
: t ≥ 0} is a symmetric diffusion semigroup on L
2(X) and denote by its tensor product extension to the Bochner space , where belongs to a certain broad class of UMD spaces. We prove a vector-valued version of the Hopf–Dunford–Schwartz ergodic theorem
and show that this extends to a maximal theorem for analytic continuations of on . As an application, we show that such continuations exhibit pointwise convergence. 相似文献
18.
We discuss the analytic properties of curves γ whose global curvature function ρ
G
[γ]−1 is p-integrable. It turns out that the L
p
-norm is an appropriate model for a self-avoidance energy interpolating between “soft” knot energies in form of singular repulsive
potentials and “hard” self-obstacles, such as a lower bound on the global radius of curvature introduced by Gonzalez and Maddocks.
We show in particular that for all p > 1 finite -energy is necessary and sufficient for W
2,p
-regularity and embeddedness of the curve. Moreover, compactness and lower-semicontinuity theorems lead to the existence of
-minimizing curves in given isotopy classes. There are obvious extensions to other variational problems for curves and nonlinearly
elastic rods, where one can introduce a bound on to preclude self-intersections. 相似文献
19.
Given
, a compact abelian group G and a function
, we identify the maximal (i.e. optimal) domain of the convolution
operator
(as an operator from Lp(G) to itself). This is the
largest Banach function space (with order continuous norm) into which Lp(G)
is embedded and to which
has a continuous extension, still with values
in Lp(G). Of course, the optimal domain depends on p and g. Whereas
is compact, this is not always so for the extension of
to its optimal domain.
Several characterizations of precisely when this is the case are presented. 相似文献
20.
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