共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper we generalize classical Lq, q≥p, estimates of the gradient to the Orlicz space for weak solutions of quasilinear elliptic equations of p-Laplacian type. 相似文献
2.
We concern with the extinction phenomenon of a non-divergent parabolic equation with a nonlinear gradient source. The critical extinction exponent of the solution is obtained. 相似文献
3.
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
4.
Frank Duzaar 《Journal of Functional Analysis》2010,259(11):2961-2998
We prove new potential and nonlinear potential pointwise gradient estimates for solutions to measure data problems, involving possibly degenerate quasilinear operators whose prototype is given by −Δpu=μ. In particular, no matter the nonlinearity of the equations considered, we show that in the case p?2 a pointwise gradient estimate is possible using standard, linear Riesz potentials. The proof is based on the identification of a natural quantity that on one hand respects the natural scaling of the problem, and on the other allows to encode the weaker coercivity properties of the operators considered, in the case p?2. In the case p>2 we prove a new gradient estimate employing nonlinear potentials of Wolff type. 相似文献
5.
6.
In this paper, the authors study the equation ut=div(|Du|p−2Du)+|u|q−1u−λl|Du| in RN with p>2. We first prove that for 1?l?p−1, the solution exists at least for a short time; then for , the existence and nonexistence of global (in time) solutions are studied in various situations. 相似文献
7.
Zhilei Liang 《Journal of Differential Equations》2009,246(1):391-134
In this paper we study the strict localization for the p-Laplacian equation with strongly nonlinear source term. Let u:=u(x,t) be a solution of the Cauchy problem
8.
Roberta Filippucci Marco Rigoli 《Journal of Mathematical Analysis and Applications》2009,356(2):689-2670
In this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of p-Laplacian elliptic inequalities, with possibly singular weights and gradient terms, of the form , under the main request that h and are continuous on R+. We achieve our conclusions introducing a generalized version of the well-known Keller-Osserman condition. 相似文献
9.
In this paper we generalize gradient estimates in Lp space to Orlicz space for weak solutions of elliptic equations of p-Laplacian type with small BMO coefficients in δ-Reifenberg flat domains. Our results improve the known results for such equations using a harmonic analysis-free technique. 相似文献
10.
11.
In this paper, we derive a local gradient estimate for the positive solution to the following parabolic equation
, where a, b are real constants, M is a complete noncompact Riemannian manifold. As a corollary, we give a local gradient estimate for the corresponding elliptic
equation:
, which improves and extends the result of Ma (J Funct Anal 241:374–382, 2006) and get a bound for the positive solution to
this elliptic equation.
相似文献
12.
Bin Qian 《数学学报(英文版)》2011,27(6):1071-1078
Let (M,g) be a complete noncompact Riemannian manifold. In this note, we derive a local Hamilton-type gradient estimate for positive
solution to a simple nonlinear parabolic equation
$
\partial _t u = \Delta u + au\log u + qu
$
\partial _t u = \Delta u + au\log u + qu
相似文献
13.
Enrico Priola 《Journal of Functional Analysis》2006,236(1):244-264
Uniform gradient estimates are derived for diffusion semigroups, possibly with potential, generated by second order elliptic operators having irregular and unbounded coefficients. We first consider the Rd-case, by using the coupling method. Due to the singularity of the coefficients, the coupling process we construct is not strongly Markovian, so that additional difficulties arise in the study. Then, more generally, we treat the case of a possibly unbounded smooth domain of Rd with Dirichlet boundary conditions. We stress that the resulting estimates are new even in the Rd-case and that the coefficients can be Hölder continuous. Our results also imply a new Liouville theorem for space-time bounded harmonic functions with respect to the underlying diffusion semigroup. 相似文献
14.
This article deals with a class of nonlocal and degenerate quasilinear parabolic equation u t = f(u)(Δu + a∫Ω u(x, t)dx ? u) with homogeneous Dirichlet boundary conditions. The local existence of positive classical solutions is proved by using the method of regularization. The global existence of positive solutions and blow-up criteria are also obtained. Furthermore, it is shown that, under certain conditions, the solutions have global blow-up property. When f(s) = s p , 0 < p ≤ 1, the blow-up rate estimates are also obtained. 相似文献
15.
For the reflected diffusion generated by on a connected and complete Riemannian manifold M with empty or convex boundary, we establish some sharp estimates of supxM|G|(x) of the Poisson equation in terms of the dimension, the diameter and the lower bound of curvature. Applications to transportation-information inequality, to Cheeger's isoperimetric inequality and to Gaussian concentration inequality are given. Several examples are provided. 相似文献
16.
17.
Xiaohong Li 《Journal of Mathematical Analysis and Applications》2011,378(2):723-733
The aim of the paper is to derive a priori estimates and obtain the Harnack-type inequalities of positive weak solutions for the nonlinear differential inequalities in an exterior domain or interior domain. By using the test function method developed by Mitidieri and Pohozaev, we extend and improve some known results proved by Serrin and Zou, Bidaut-Véron and Pohozaev. 相似文献
18.
Yi Zhan 《应用数学学报(英文版)》1997,13(2):136-144
In this part we construct a unique bounded Hölder continuous viscosity solution for the nonlinear PDEs with the evolutionp-Laplacian equation and its anisotropic version as typical examples. The existence and properties of free boundaries will be discussed in part II.This research is supported by the National Natural Sciences Foundation of China. 相似文献
19.
Let A,B:(0,∞)?(0,∞) be two given weight functions and consider the equation
20.
We investigate the existence of nonnegative weak solutions to the problem ut=Δ(um)−p|∇u| in Rn×(0,∞) with +(1−2/n)<m<1. It will be proved that: (i) When 1<p<2, if the initial datum u0∈D(Rn) then there exists a solution; (ii) When 1<p<(2+mn)/(n+1), if the initial datum u0(x) is a bounded and nonnegative measure then the solution exists; (iii) When (2+mn)/(n+1)?p<2, if the initial datum is a Dirac mass then the solution does not exist. We also study the large time behavior of the L1-norm of solutions for 1<p?(2+mn)/(n+1), and the large time behavior of t1/β‖u(⋅,t)−Ec(⋅,t)L∞‖ for (2+mn)/(n+1)<p<2. 相似文献
|