Harnack inequality and regularity of $p$-Laplace equation on complete manifolds
نویسندگان
چکیده
منابع مشابه
Harnack Inequality for Nondivergent Elliptic Operators on Riemannian Manifolds
We consider second-order linear elliptic operators of nondivergence type which is intrinsically defined on Riemannian manifolds. Cabré proved a global Krylov-Safonov Harnack inequality under the assumption that the sectional curvature is nonnegative. We improve Cabré’s result and, as a consequence, we give another proof to Harnack inequality of Yau for positive harmonic functions on Riemannian ...
متن کاملDifferential Harnack Inequalities on Riemannian Manifolds I : Linear Heat Equation
Abstract. In the first part of this paper, we get new Li-Yau type gradient estimates for positive solutions of heat equation on Riemmannian manifolds with Ricci(M) ≥ −k, k ∈ R. As applications, several parabolic Harnack inequalities are obtained and they lead to new estimates on heat kernels of manifolds with Ricci curvature bounded from below. In the second part, we establish a Perelman type L...
متن کاملBoundary Harnack principle and elliptic Harnack inequality
We prove a scale-invariant boundary Harnack principle for inner uniform domains over a large family of Dirichlet spaces. A novel feature of our work is that our assumptions are robust to time changes of the corresponding diffusions. In particular, we do not assume volume doubling property for the symmetric measure.
متن کاملHarnack type inequality for positive solution of some integral equation
In this paper, we establish some Harnack type inequalities satisfied by positive solutions of nonlocal inhomogeneous equations arising in the description of various phenomena ranging from population dynamics to micro-magnetism. For regular domains, we also derive an inequality up to the boundary. The main difficulty in such context lies in a precise control of the solutions outside a compact se...
متن کاملHarnack Inequality on Homogeneous Spaces
We consider a connected, locally compact topological space X. We suppose that a pseudo-distance d is defined on X that is, d : X × X 7−→ R+ such that d (x, y) > 0 if and only if x 6= y; d (x, y) = d (y, x) ; d (x, z) ≤ γ [d (x, y) + d (y, z)] for all x, y, z ∈ X, where γ ≥ 1 is some given constant and we suppose that the pseudo-balls B (x, r) = {y ∈ X : d (x, y) < r} , r > 0, form a basis of op...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Kodai Mathematical Journal
سال: 2000
ISSN: 0386-5991
DOI: 10.2996/kmj/1138044262