Evolution Equations on a Riemannian Manifold with a Lower Ricci Curvature Bound
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We consider the parabolic evolution differential equations such as heat equation and porus-medium equation on a Riemannian manifold $M$ whose Ricci curvature is bounded below by $-(n-1)k^2$ and bounded below by $0$ on some amount of $M$. We derive some bounds of differential quantities for a positive solution and some inequalities which resemble Harnack inequalities.
Abstract
We consider the parabolic evolution differential equations such as heat equation and porus-medium equation on a Riemannian manifold $M$ whose Ricci curvature is bounded below by $-(n-1)k^2$ and bounded below by $0$ on some amount of $M$. We derive some bounds of differential quantities for a positive solution and some inequalities which resemble Harnack inequalities.
참고문헌 (7)
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