相关论文: Stability of parabolic Harnack inequalities on met…

We prove that the elliptic Harnack inequality (on a manifold, graph, or suitably regular metric measure space) is stable under bounded perturbations, as well as rough isometries.

In this paper, we establish stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms on metric measure spaces under general volume doubling condition. We obtain their stable equivalent characterizations in terms…

We study relations and characterizations of various elliptic Harnack inequalities for symmetric non-local Dirichlet forms on metric measure spaces. We allow the scaling function be state-dependent and the state space possibly disconnected.…

We show that elliptic Harnack inequality is stable under form-bounded perturbations for strongly local Dirichlet forms on complete locally compact separable metric spaces that satisfy metric doubling property (or equivalently, relative ball…

This paper proves the strong parabolic Harnack inequality for local weak solutions to the heat equation associated with time-dependent (nonsymmetric) bilinear forms. The underlying metric measure Dirichlet space is assumed to satisfy the…

We study weak Harnack inequality and a priori H\"older regularity of harmonic functions for symmetric nonlocal Dirichlet forms on metric measure spaces with volume doubling condition. Our analysis relies on three main assumptions: the…

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…

In the context of a metric measure Dirichlet space satisfying volume doubling and Poincar\'e inequality, we prove the parabolic Harnack inequality for weak solutions of the heat equation associated with local nonsymmetric bilinear forms. In…

In this paper, we establish a scale invariant Harnack inequality for some inhomogeneous parabolic equations in a suitable intrinsic geometry dictated by the nonlinearity. The class of equations that we consider correspond to the parabolic…

We study parabolic operators H = $\partial$t -- div $\lambda$,x A(x, t)$\nabla$ $\lambda$,x in the parabolic upper half space R n+2 + = {($\lambda$, x, t) : $\lambda$ > 0}. We assume that the coefficients are real, bounded, measurable,…

We consider a homogeneous space $X=(X,d,m) $ of dimension $\nu\geq1$ and a local regular Dirichlet form in $L^{2}(X,m) .$ We prove that if a Poincar\'{e} inequality holds on every pseudo-ball $B(x,R) $ of $X$, then an Harnack's inequality…

We prove a stability theorem for the elliptic Harnack inequality: if two weighted graphs are equivalent, then the elliptic Harnack inequality holds for harmonic functions with respect to one of the graphs if and only if it holds for…

It is known that solutions to second order uniformly elliptic and parabolic equations, either in divergence or nondivergence (general) form, are H\"{o}lder continuous and satisfy the interior Harnack inequality. We show that even in the…

Consider a symmetric Markovian jump process $\{X_t\}$ on a metric measure space $(M, d, \mu)$. Chen, Kumagai, and Wang recently showed that two-sided heat kernel estimates and the parabolic Harnack inequality are both stable under bounded…

We establish a Harnack inequality for a class of quasi-linear PDE modeled on the prototype {equation*} \partial_tu= -\sum_{i=1}^{m}X_i^\ast (|\X u|^{p-2} X_i u){equation*} where $p\ge 2$, $ \ \X = (X_1,..., X_m)$ is a system of Lipschitz…

In this paper we continue the study on intrinsic Harnack inequality for non- homogeneous parabolic equations in non-divergence form initiated by the first author in [1]. We establish a forward-in-time intrinsic Harnack inequality, which in…

This paper provides the general theory on parabolic Harnack inequalities (PHI, for short) for regular Dirichlet forms without killing part. We prove PHI by pure analytic methods, using both Nash and Moser approaches, and yield some…

We settle the open question concerning the Harnack inequality for globally positive solutions to non-local in time diffusion equations by constructing a counter-example for dimensions $d\ge\beta$, where $\beta\in(0,2]$ is the order of the…

In this paper we study problems related to parabolic partial differential equations in metric measure spaces equipped with a doubling measure and supporting a Poincare' inequality. We give a definition of parabolic De Giorgi classes and…

In this paper we give equivalent conditions for the weak parabolic Harnack inequality for general regular Dirichlet forms without killing part, in terms of local heat kernel estimates or growth lemmas. With a tail estimate on the jump…