共查询到20条相似文献,搜索用时 21 毫秒
1.
We provide a representation for strong-weak continuous dynamic risk measures from Lp into Lpt spaces where these spaces are equipped respectively with strong and weak topologies and p is a finite number strictly larger than one. Conversely, we show that any such representation that admits a compact (with respect to the product of weak topologies) sub-differential generates a dynamic risk measure that is strong--weak continuous. Furthermore, we investigate sufficient conditions on the sub-differential for which the essential supremum of the representation is attained. Finally, the main purpose is to show that any convex dynamic risk measure that is strong-weak continuous can be approximated by a sequence of convex dynamic risk measures which are strong--weak continuous and admit compact sub-differentials with respect to the product of weak topologies. Throughout the arguments, no conditional translation invariance or monotonicity assumptions are applied. 相似文献
2.
Parinya Sa Ngiamsunthorn 《Journal of Evolution Equations》2012,12(1):1-26
The aim of this paper is to study the behavior of bounded solutions of parabolic equations on the whole real line under perturbation
of the underlying domain. We give the convergence of bounded solutions of linear parabolic equations in the L
2 and the L
p
-settings. For the L
p
-theory, we also prove the H?lder regularity of bounded solutions with respect to time. In addition, we study the persistence
of a class of bounded solutions which decay to zero at t → ±∞ of semilinear parabolic equations under domain perturbation. 相似文献
3.
4.
In this paper, we discuss the existence and uniqueness of solutions of the constrained variational problem with respect to the fractional Kirchhoff equation. For the exponent p<p*(s,N), a complete classification with respect to p for the existence of solutions of the fractional Kirchhoff functional on the L2-normalized manifold was given. Furthermore, all these solutions are unique up to translations, and our methods depend only on some simple energy estimates. 相似文献
5.
We prove existence of strong solutions of Pucci extremal equations with superlinear growth in Du and unbounded coefficients. We apply this result to establish the weak Harnack inequality for Lp-viscosity supersolutions of fully nonlinear uniformly elliptic PDEs with superlinear growth terms with respect to Du.
相似文献
6.
Atanas Stefanov 《Journal of Fourier Analysis and Applications》2010,16(1):97-128
In this work, we develop L
p
boundedness theory for pseudodifferential operators with rough (not even continuous in general) symbols in the x variable. Moreover, the B(L
p
) operator norms are estimated explicitly in terms of scale invariant quantities involving the symbols. All the estimates
are shown to be sharp with respect to the required smoothness in the ξ variable. As a corollary, we obtain L
p
bounds for (smoothed out versions of) the maximal directional Hilbert transform and the Carleson operator. 相似文献
7.
We derive interior L
p
-estimates for solutions of linear elliptic systems with oscillatory coefficients. The estimates are independent of ε, the small length scale of the rapid oscillations. So far, such results are based on potential theory and restricted to periodic
coefficients. Our approach relies on BMO-estimates and an interpolation argument, gradients are treated with the help of finite
differences. This allows to treat coefficients that depend on a fast and a slow variable. The estimates imply an L
p
-corrector result for approximate solutions.
相似文献
8.
In this paper, we are concerned with the stochastic differential delay equations with Markovian switching (SDDEwMSs). As stochastic differential equations with Markovian switching (SDEwMSs), most SDDEwMSs cannot be solved explicitly. Therefore, numerical solutions, such as EM method, stochastic Theta method, Split-Step Backward Euler method and Caratheodory’s approximations, have become an important issue in the study of SDDEwMSs. The key contribution of this paper is to investigate the strong convergence between the true solutions and the numerical solutions to SDDEwMSs in the sense of the Lp-norm when the drift and diffusion coefficients are Taylor approximations. 相似文献
9.
For the problem of diffraction of harmonic scalar waves by a lossless periodic slab scatterer, we analyze field sensitivity with respect to the material coefficients of the slab. The governing equation is the Helmholtz equation, which describes acoustic or electromagnetic fields. The main theorem establishes the variational (Fréchet) derivative of the scattered field measured in the H1 (root-mean-square-gradient) norm as a function of the material coefficients measured in an Lp (p-power integral) norm, with 2<p<∞, as long as these coefficients are bounded above and below by positive constants and do not admit resonance. The derivative is Lipschitz continuous. We also establish the variational derivative of the transmitted energy with respect to the material coefficients in Lp. 相似文献
10.
Fengping Yao 《Mathematische Nachrichten》2010,283(9):1358-1367
In this paper we generalize global Lp‐type gradient estimates to Orlicz spaces for weak solutions of the parabolic equations with small BMO coefficients in Reifenberg flat domains (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
12.
In this article, we study a second-order differential operator with mixed nonlocal boundary conditions combined weighting integral boundary condition with another two-point boundary condition. Under certain conditions on the weighting functions and on the coefficients in the boundary conditions, called regular and nonregular cases, we prove that the resolvent decreases with respect to the spectral parameter in L p ?(0,?1), but there is no maximal decreasing at infinity for p?>?1. Furthermore, the studied operator generates in L p ?(0,?1) an analytic semigroup for p?=?1 in regular case, and an analytic semigroup with singularities for p?>?1 in both cases, and for p?=?1 in the nonregular case only. The obtained results are then used to show the correct solvability of a mixed problem for a parabolic partial differential equation with nonregular boundary conditions. 相似文献
13.
Yu. A. Kordyukov 《Acta Appl Math》1991,23(3):223-260
This paper is devoted to some of the properties of uniformly elliptic differential operators with bounded coefficients on manifolds of bounded geometry in L
pspaces. We prove the coincidence of minimal and maximal extensions of an operator of a considered type with a positive principal symbol, the existence of holomorphic semigroup, generated by it, and the estimates of L
p-norms of the operators of this semigroup. Some spectral properties of such operators in L
pspaces are also studied. 相似文献
14.
Pointwise convergence of double trigonometric Fourier series of functions in the Lebesgue space L
p[0,2]2was studied by M. I. Dyachenko. In this paper, we also consider the problems of the convergence of double Fourier series in Pringsheim"s sense with respect to the trigonometric as well as the Walsh systems of functions in the Lebesgue space L
p[0,1]2, p=(p1,p2), endowed with a mixed norm, in the particular case when the coefficients of the series in question are monotone with respect to each of the indices. We shall obtain theorems which generalize those of M. I. Dyachenko to the case when p is a vector. We shall also show that our theorems in the case of trigonometric Fourier series are best possible. 相似文献
15.
Shaokuan Chen 《随机分析与应用》2013,31(5):820-841
In this article, we study one-dimensional backward stochastic differential equations with continuous coefficients. We show that if the generator f is uniformly continuous in (y, z), uniformly with respect to (t, ω), and if the terminal value ξ ∈L p (Ω, ? T , P) with 1 < p ≤ 2, the backward stochastic differential equation has a unique L p solution. 相似文献
16.
Matthias Geissert Luca Lorenzi Roland Schnaubelt 《Annali di Matematica Pura ed Applicata》2010,189(2):303-333
We establish the maximal regularity for nonautonomous Ornstein–Uhlenbeck operators in L p -spaces with respect to a family of invariant measures, where ${p \in (1, +\infty)}We establish the maximal regularity for nonautonomous Ornstein–Uhlenbeck operators in
L
p
-spaces with respect to a family of invariant measures, where p ? (1, +¥){p \in (1, +\infty)} . This result follows from the maximal L
p
-regularity for a class of elliptic operators with unbounded, time-dependent drift coefficients and potentials acting on
Lp(\mathbbRN ){L^{p}(\mathbb{R}^{N} )} with Lebesgue measure. 相似文献
17.
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
18.
We show that theL
p
norms, 0<p<∞, of the nontangenital maximal function and area integral of solutions and normalized adjoint solutions to second order
nondivergence form elliptic equations, are comparable when integrated on the boundary of a Lipschitz domain with respect to
measures, which are respectivelyA
∞ with respect to the corresponding harmonic measure or normalized harmonic measure.
Both authors are supported by NSF 相似文献
19.
The first object of this paper is to introduce a new evolution equation for the characteristic function of the boundary Γ
of a Lipschitzian domain Ω in the N-dimensional Euclidean space under the influence of a smooth time-dependent velocity field. The originality of this equation is that the evolution takes place in an Lp-space with respect to the (N − 1)-Hausdorff measure. A second more speculative objective is to discuss how that equation can be relaxed to rougher velocity
fields via some weak formulation. A candidate is presented and some of the technical difficulties and open issues are discussed.
Continuity results in several metric topologies are also presented. The paper also specializes the results on the evolution
of the oriented distance function to initial sets with zero N-dimensional Lebesgue measure. 相似文献
20.
Michael Ruzhansky 《Results in Mathematics》2002,41(3-4):361-368
In this paper we consider the Cauchy problem for a class of hyperbolic pseudodifferential operators. The considered class contains constant coefficient differential equations, also allowing the coefficients to depend on time. We establish sharp L p ? Lp, Lipschitz, and other estimates for their solutions. In particular, the ellipticity condition for the roots of the principal symbol is eliminated for certain dimensions. We discuss the situation with no loss of smoothness for solutions. In the space R1+n with n ≤ 4 (total dimension ≤ 5), we give a complete list of L p ? Lp properties. In particular, this contains the very important case R1+3. 相似文献