共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
I. T. Mamedov 《Mathematical Notes》1976,20(5):961-965
The paper considers a second-order linear parabolic equation whose coefficients satisfy a Dini condition. It is proven that the conditions for regularity of the boundary points for such an equation and for the heat-conduction equation coincide.Translated from Matematicheskie Zametki, Vol. 20, No. 5, pp. 717–723, November, 1976. 相似文献
3.
Density of Lipschitz functions in Newtonian spaces based on quasi-Banach function lattices is discussed. Newtonian spaces are first-order Sobolevtype spaces on abstract metric measure spaces defined via (weak) upper gradients. Our main focus lies on metric spaces with a doubling measure that support a Poincaré inequality. Absolute continuity of the function lattice quasi-norm is shown to be crucial for approximability by (locally) Lipschitz functions. The proof of the density result uses, among other facts, the fact that a suitable maximal operator is locally weakly bounded. In particular, various sufficient conditions for such boundedness on quasi-Banach function lattices (and rearrangement-invariant spaces, in particular) are established and applied. 相似文献
4.
Yuqing Yan 《Journal of Mathematical Analysis and Applications》2018,457(1):248-272
By a dual method, two Carleman estimates for forward and backward stochastic parabolic equations with Neumann boundary conditions are established. Then they are used to study a null controllability problem and a state observation problem for some stochastic forward parabolic equations with Neumann boundary conditions. 相似文献
5.
Paolo Baroni Agnese Di Castro Giampiero Palatucci 《Journal of Evolution Equations》2013,13(1):163-195
We consider nonlinear parabolic equations of the type $$u_t - {\rm div}a(x, t, Du)= f(x, t) \quad {\rm on}\quad \Omega_T =\Omega\times (-T,0),$$ under standard growth conditions on a, with f only assumed to be integrable. We prove general decay estimates up to the boundary for level sets of the solutions u and the gradient Du which imply very general estimates in Lebesgue and Lorentz spaces. Assuming only that the involved domains satisfy a mild exterior capacity density condition, we provide global regularity results. 相似文献
6.
A. V. Ivanov 《Journal of Mathematical Sciences》1999,93(5):661-688
Local gradient estimates for weak solutions of the equation
are established in the case m>1, 0≤l<1. In the case m>1, l≥1, some weight gradient estimates are obtained. Bibliography:
19 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 233, 1996, pp. 63–100. 相似文献
7.
8.
Summary Wiener estimates at a point for parabolic diagonal systems of parabolic variational inequalities with obstacle are proved by a Green function method.This paper was written while the first Author was visiting the Department of Mathematics of Linköping University. 相似文献
9.
10.
Maria Manfredini Andrea Pascucci 《Proceedings of the American Mathematical Society》2003,131(4):1115-1120
We prove some maximum and gradient estimates for classical solutions to a wide class of quasilinear degenerate parabolic equations, including first order ones. The proof is elementary and exploits the smallness of the domain in the time direction.
11.
We establish the intrinsic Harnack inequality for non-negative solutions of a class of degenerate, quasilinear, parabolic equations, including equations of the p-Laplacian and porous medium type. It is shown that the classical Harnack estimate, while failing for degenerate parabolic equations, it continues to hold in a space-time geometry intrinsic to the degeneracy. The proof uses only measure-theoretical arguments, it reproduces the classical Moser theory, for non-degenerate equations, and it is novel even in that context. Hölder estimates are derived as a consequence of the Harnack inequality. The results solve a long standing problem in the theory of degenerate parabolic equations. 相似文献
12.
13.
Of concern is the uniformly parabolic problem
14.
15.
16.
17.
Hongjie Dong Seick Kim 《Calculus of Variations and Partial Differential Equations》2011,40(3-4):481-500
We establish Schauder estimates for both divergence and non-divergence form second-order elliptic and parabolic equations involving H?lder semi-norms not with respect to all, but only with respect to some of the independent variables. 相似文献
18.
M. D. Surnachev 《Proceedings of the Steklov Institute of Mathematics》2012,278(1):241-250
We obtain improved pointwise estimates for solutions to nonlinear parabolic equations with double degeneracy. These estimates differ from the classical estimates known for the linear case in that the supremum of the modulus of a solution is estimated by the sum of two powers of the integral norm of the solution. 相似文献
19.
Fengping Yao 《Journal of Mathematical Analysis and Applications》2010,364(2):576-590
In this paper optimal regularity estimates for weak solutions of quasilinear parabolic equations of p-Laplacian type with small BMO coefficients are investigated. Our results improve the known results for such equations using a harmonic analysis free technique. 相似文献
20.
《Mathematische Nachrichten》2018,291(5-6):996-1008
We prove a global Lorentz estimate of the Hessian of strong solutions to the Cauchy–Dirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded C1, 1 domain. Here, we mainly assume that the associated regular nonlinearity satisfies uniformly parabolicity and the ‐vanishing condition, and the approach of constructing a regular problem by an appropriate transformation is employed. 相似文献