共查询到20条相似文献,搜索用时 31 毫秒
1.
Minoru Murata 《Journal of Functional Analysis》2002,194(1):53-141
We consider positive solutions of elliptic partial differential equations on non-compact domains of Riemannian manifolds. We explicitly determine Martin boundaries and Martin kernels for a class of elliptic equations in skew product form by exploiting and developing perturbation theory for elliptic equations and short/long-time estimates for fundamental solutions of parabolic equations. 相似文献
2.
Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients
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Hongjie Dong 《分析论及其应用》2020,36(2):161-199
In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $\rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations. 相似文献
3.
Boundedness in Morrey spaces is studied for singular integral operators with kernels of mixed homogeneity and their commutators with multiplication by a BMO-function. The results are applied in obtaining fine (Morrey and Hölder) regularity of strong solutions to higher-order elliptic and parabolic equations with VMO coefficients. 相似文献
4.
We prove generalized Aleksandrov–Bakelman–Pucci maximum principles for elliptic and parabolic integro-PDEs of Hamilton–Jacobi–Bellman–Isaacs types, whose PDE parts are either uniformly elliptic or uniformly parabolic. The proofs of these results are based on the classical Aleksandrov–Bakelman–Pucci maximum principles for the elliptic and parabolic PDEs and an iteration procedure using solutions of Pucci extremal equations. We also provide proofs of nonlocal versions of the classical Aleksandrov–Bakelman–Pucci maximum principles for elliptic and parabolic integro-PDEs. 相似文献
5.
Jason J. Sharples 《Journal of Differential Equations》2004,202(1):111-142
We consider linear parabolic equations of second order in a Sobolev space setting. We obtain existence and uniqueness results for such equations on a closed two-dimensional manifold, with minimal assumptions about the regularity of the coefficients of the elliptic operator. In particular, we derive a priori estimates relating the Sobolev regularity of the coefficients of the elliptic operator to that of the solution. The results obtained are used in conjunction with an iteration argument to yield existence results for quasilinear parabolic equations. 相似文献
6.
半线性椭圆方程支配系统的最优性条件 总被引:2,自引:0,他引:2
本文讨论了可能具有多值解的椭圆型偏微分方程支配系统的最优控制问题,我们通过构造一个抛物方程控制问题的逼近序列,并利用抛物方程控制问题的结果,得到了椭圆系统最优控制的必要条件. 相似文献
7.
Zhen-Qing Chen 《中国科学A辑(英文版)》2009,52(7):1423-1445
We survey the recent development of the DeGiorgi-Nash-Moser-Aronson type theory for a class of symmetric jump processes (or equivalently, a class of symmetric integro-differential operators). We focus on the sharp two-sided estimates for the transition density functions (or heat kernels) of the processes, a priori Hölder estimate and parabolic Harnack inequalities for their parabolic functions. In contrast to the second order elliptic differential operator case, the methods to establish these properties for symmetric integro-differential operators are mainly probabilistic. 相似文献
8.
We establish Hölder estimates for the time derivative of solutions of nonlocal parabolic equations under mild assumptions for the boundary data. As a consequence we are able to extend the Evans‐Krylov estimate for rough kernels to parabolic equations. © 2016 Wiley Periodicals, Inc. 相似文献
9.
Hans D. Mittelmann 《Computational Optimization and Applications》2001,20(1):93-110
We study optimal control problems for semilinear parabolic equations subject to control constraints and for semilinear elliptic equations subject to control and state constraints. We quote known second-order sufficient optimality conditions (SSC) from the literature. Both problem classes, the parabolic one with boundary control and the elliptic one with boundary or distributed control, are discretized by a finite difference method. The discrete SSC are stated and numerically verified in all cases providing an indication of optimality where only necessary conditions had been studied before. 相似文献
10.
A. V. Masley 《Siberian Mathematical Journal》2013,54(5):857-870
Every element in PSL(2, ?) is elliptic, parabolic, or loxodromic. For the groups generated by two elliptic elements, sufficient discreteness conditions were obtained by Gehring, Maclachlan, Martin, and Rasskazov. In this article we establish sufficient discreteness conditions for the groups generated by two loxodromic elements and the groups generated by a loxodromic element and an elliptic element. 相似文献
11.
In this paper we obtain the global regularity estimates of the solutions in Sobolev spaces and Orlicz spaces for higher-order elliptic and parabolic equations of nondivergence form in the whole space. We only need to focus on the parabolic case since the corresponding result in the elliptic case can be obtained as a corollary. 相似文献
12.
鲁又文 《纯粹数学与应用数学》1994,(2)
设Ω为En中的无界,连通区域.在Ω×(0,∞)上考虑抛物型方程:设,B满足结构条件:设存在和,使对任何ρ0>ρ1>0:设u是方程的广义解,并且如果u在Ω×(0,T)为有界,那么u+≤0. 相似文献
13.
In this paper we obtain the global regularity estimates of the weak solutions in Sobolev spaces and Orlicz spaces for higher order elliptic and parabolic equations of divergence form with small BMO coefficients in the whole space. We only focus on the parabolic case while the corresponding result in the elliptic case can be obtained as a corollary. 相似文献
14.
M. Kubo K. Shirakawa N. Yamazaki 《Journal of Mathematical Analysis and Applications》2012,387(2):490-511
We create a general framework for mathematical study of variational inequalities for a system of elliptic–parabolic equations. In this paper, we establish a solvability theorem concerning the existence of solutions for the vector-valued elliptic–parabolic variational inequality with time-dependent constraint. Moreover, we give some applications of the system, for example, time-dependent boundary obstacle problem and time-dependent interior obstacle problem. 相似文献
15.
We consider parabolic operators of fractional order and their iterates on the upper half space of the euclidean space. We deal with Hilbert spaces of solutions of those parabolic equations. We shall show, in this note, the existence of reproducing kernels and give a formula by using their fundamental solutions. As an application, we also discuss the polyharmonic Bergman spaces and give their reproducing kernels by using the Poisson kernel on the upper half space. 相似文献
16.
In this paper, we consider the Neumann problem for parabolic Hessian quotient equations.We show that the k-admissible solution of the parabolic Hessian quotient equation exists for all time and converges to the smooth solution of elliptic Hessian quotient equations. Also solutions of the classical Neumann problem converge to a translating solution. 相似文献
17.
O. Casas-Sánchez W. A. Zúñiga-Galindo 《P-Adic Numbers, Ultrametric Analysis, and Applications》2013,5(3):177-193
We study pseudodifferential equations and Riesz kernels attached to certain quadratic forms over p-adic fields. We attach to an elliptic quadratic form of dimension two or four a family of distributions depending on a complex parameter, the Riesz kernels, and show that these distributions form an Abelian group under convolution. This result implies the existence of fundamental solutions for certain pseudodifferential equations like in the classical case. 相似文献
18.
Yurii V. Brezhnev 《Journal of Differential Equations》2012,253(12):3727-3751
We show that four exceptional Fuchsian equations, each determined by the four parabolic singularities, known as the Chudnovsky equations, are transformed into each other by algebraic transformations. We describe equivalence of these equations and their counterparts on tori. The latters are the Fuchsian equations on elliptic curves and their equivalence is characterized by transcendental transformations which are represented explicitly in terms of elliptic and theta functions. 相似文献
19.
Jessica Lin 《偏微分方程通讯》2015,40(9):1688-1704
This note establishes an interior quantitative lower bound for nonnegative supersolutions of fully nonlinear uniformly parabolic equations. The result may be interpreted as a quantitative version of a growth lemma established by Krylov and Safonov for nonnegative supersolutions of linear uniformly parabolic equations in nondivergence form. Our approach is different, and follows from an application of a reverse Holder inequality. The result is the parabolic analogue of an elliptic regularity estimate established by Caffarelli, Souganidis, and Wang in the stochastic homogenization of fully nonlinear uniformly elliptic equations. 相似文献
20.
Pierre Gilles Lemarié-Rieusset 《Journal of Functional Analysis》2018,274(3):659-694
We develop a general framework to describe global mild solutions to a Cauchy problem with small initial values concerning a general class of semilinear parabolic equations with a quadratic nonlinearity. This class includes the Navier–Stokes equations, the subcritical dissipative quasi-geostrophic equation and the parabolic–elliptic Keller–Segel system. 相似文献