Results 1 to 10 of about 472,112 (168)

Harnack inequality for a class of functionals with non-standard growth via De Giorgi’s method

Advances in Nonlinear Analysis, 2018
We study the regularity theory of quasi-minimizers of functionals with Lp⁢(⋅)⁢log⁡L{L^{p(\,\cdot\,)}\log L}-growth. In particular, we prove the Harnack inequality and, in addition, the local boundedness and the Hölder continuity of the quasi-minimizers ...
Jihoon Ok
exaly   +2 more sources

Bilateral Harnack Inequalities for Stochastic Differential Equation with Multiplicative Noise

Journal of Function Spaces, 2022
By constructing a coupling with unbounded time-dependent drift, a lower bound estimate of dimension-free Harnack inequality with power is obtained for a large class of stochastic differential equation with multiplicative noise.
Zihao An, Gaofeng Zong
doaj   +1 more source

Regularity estimates for fractional orthotropic p-Laplacians of mixed order

Advances in Nonlinear Analysis, 2022
We study robust regularity estimates for a class of nonlinear integro-differential operators with anisotropic and singular kernels. In this paper, we prove a Sobolev-type inequality, a weak Harnack inequality, and a local Hölder estimate.
Chaker Jamil, Kim Minhyun
doaj   +1 more source

Harnack Estimation for Nonlinear, Weighted, Heat-Type Equation along Geometric Flow and Applications

Mathematics, 2023
The method of gradient estimation for the heat-type equation using the Harnack quantity is a classical approach used for understanding the nature of the solution of these heat-type equations. Most of the studies in this field involve the Laplace–Beltrami
Yanlin Li, Sujit Bhattacharyya, Shahroud Azami, Apurba Saha, Shyamal Kumar Hui   +4 more
doaj   +1 more source

Li–Yau-Type Gradient Estimate along Geometric Flow

Mathematics, 2023
In this article we derive a Li–Yau-type gradient estimate for a generalized weighted parabolic heat equation with potential on a weighted Riemannian manifold evolving by a geometric flow.
Shyamal Kumar Hui, Abimbola Abolarinwa, Meraj Ali Khan, Fatemah Mofarreh, Apurba Saha, Sujit Bhattacharyya   +5 more
doaj   +1 more source

Improved bounds for solutions of ϕ-Laplacians [PDF]

Opuscula Mathematica, 2018
In this short paper we prove a parametric version of the Harnack inequality for \(\phi\)-Laplacian equations. In this sense, the estimates are optimal and represent an improvement of previous bounds for this kind of operators.
Waldo Arriagada, Jorge Huentutripay
doaj   +1 more source

On the continuity of solutions to advection-diffusion equations with slightly super-critical divergence-free drifts

Advances in Nonlinear Analysis, 2014
We address the regularity of solutions to elliptic and parabolic equations of the form -Δu+b·∇u=0${- \Delta u+b\cdot \nabla u=0}$ and ut-Δu+b·∇u=0${u_t- \Delta u+b\cdot \nabla u=0}$ with divergence-free drifts b.
Ignatova Mihaela
doaj   +1 more source

Reverse Smoothing Effects, Fine Asymptotics, and Harnack Inequalities for Fast Diffusion Equations

Boundary Value Problems, 2006
We investigate local and global properties of positive solutions to the fast diffusion equation ut=Δum in the good exponent range (d−2 ...
Juan Luis Vazquez, Matteo Bonforte
doaj   +1 more source

A short note on Harnack inequality for k-Hessian equations with nonlinear gradient terms [PDF]

Opuscula Mathematica
In this short note we study a Harnack inequality for \(k\)-Hessian equations that involve nonlinear lower-order terms which depend on the solution and its gradient.
Ahmed Mohammed, Giovanni Porru
doaj   +1 more source

Qualitative Analysis of a Three-Species Reaction-Diffusion Model with Modified Leslie-Gower Scheme

Journal of Function Spaces, 2021
The qualitative analysis of a three-species reaction-diffusion model with a modified Leslie-Gower scheme under the Neumann boundary condition is obtained.
Xiaoni Wang, Gaihui Guo, Jian Li, Mengmeng Du   +3 more
doaj   +1 more source