Related papers: A Harnack's inequality for mixed type evolution eq…

We prove invariant Harnack inequalities for certain classes of non-divergence form equations of Kolmogorov type. The operators we consider exhibit invariance properties with respect to a homogeneous Lie group structure. The coefficient…

We study local regularity for nonlocal doubly degenerate parabolic equations. The model equation is \begin{equation*}\begin{split}…

We prove the intrinsic Harnack's inequality for a general form of a parabolic equation that generalizes both the standard parabolic $p$-Laplace equation and the normalized version arising from stochastic game theory. We prove each result…

We study a class of second-order degenerate linear parabolic equations in divergence form in $(-\infty, T) \times \mathbb R^d_+$ with homogeneous Dirichlet boundary condition on $(-\infty, T) \times \partial \mathbb R^d_+$, where $\mathbb…

We complete the local regularity program for weak solutions to linear parabolic nonlocal equations with bounded measurable coefficients. Within the variational framework we prove the parabolic Harnack inequality and H\"older regularity…

We study quasilinear evolutionary partial integro-differential equations of second order which include time fractional $p$-Laplace equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration…

We study a class of nondivergence form second-order degenerate linear parabolic equations in $(-\infty, T) \times {\mathbb R}^d_+$ with the homogeneous Dirichlet boundary condition on $(-\infty, T) \times \partial {\mathbb R}^d_+$, where…

We give a unified proof of H\"{o}lder regularity of weak solutions for mixed local and nonlocal $p$-Laplace type parabolic equations with the full range of exponents $1<p<\infty$. Our proof is based on the expansion of positivity together…

This paper aims to investigate a Harnack inequality for non-negative solutions of the normalized infinity Laplacian with nonlinear absorption and gradient terms. More specifically, we establish a Harnack inequality for non-negative…

We study inhomogeneous semilinear parabolic equations with source term f independent of time u_{t}={\Delta}u+u^{p}+f(x) on a metric measure space, subject to the conditions that f(x)\geq 0 and u(0,x)=\phi(x)\geq 0. By establishing…

We prove a Harnack inequality for the solutions of a difference equation with non-elliptic balanced i.i.d. coefficients. Along the way we prove a (weak) quantitative homogenisation result, which we believe is of some interest too.

We prove Harnack's inequality for bounded weak solutions to quasilinear second order elliptic equations with generalized Orlicz growth conditions. Our approach covers new cases of variable exponent and (p,q) growth conditions.

Motivated by the Onsager statistical mechanics description of turbulent Euler flows with point singularities, we obtain a Harnack-type inequality for sequences of solutions of the following perturbed Liouville equation,…

In this paper we study the global boundedness for the solutions to a class of possibly degenerate parabolic equations by De-Giorgi's iteration. As applications, we show the existence of weak solutions for possibly degenerate stochastic…

In a cylinder $\Omega_T=\Omega\times (0,T)\subset \R^{n+1}_+$ we study the boundary behavior of nonnegative solutions of second order parabolic equations of the form \[ Hu =\sum_{i,j=1}^ma_{ij}(x,t) X_iX_ju - \p_tu = 0, \…

We consider subelliptic equations in non divergence form of the type $Lu = \sum a_{ij} X_jX_iu=0$, where $X_j$ are the Grushin vector fields, and the matrix coefficient is uniformly elliptic. We obtain a scale invariant Harnack's inequality…

We prove an elliptic Harnack's inequality for a general form of a parabolic equation that generalizes both the standard parabolic $p$-Laplace equation and the normalized version that has been proposed in stochastic game theory. This version…

We give a direct analytic proof of the classical Boundary Harnack inequality for solutions to linear uniformly elliptic equations in either divergence or non-divergence form.

Let $\Omega \subset \mathbb R^N$, $N \geq 2$, be a smooth bounded domain. We consider a boundary value problem of the form $$-\Delta u = c_{\lambda}(x) u + \mu(x) |\nabla u|^2 + h(x), \quad u \in H^1_0(\Omega)\cap L^{\infty}(\Omega)$$ where…

We establish Harnack inequalities for viscosity solutions of a class of degenerate fully nonlinear anisotropic elliptic equations exhibiting non-standard growth conditions. A primary example of such operators is the degenerate anisotropic…