Related papers: On generalized Li-Yau inequalities

By using lower bound conditions of the L\'evy measure, derivative formulae and Harnack inequalities are derived for linear stochastic differential equations driven by L\'evy processes. As applications, explicit gradient estimates and heat…

We present a generalization of a formula of higher order derivatives and give a short proof.

We consider the linear heat equation on a bounded domain and on an exterior domain. We study estimates of any order derivatives of the solution locally in time in the Lebesgue spaces. We give a proof of the estimates in the end-point cases…

We give a generalization of Yamaguchi--Yau's result to Walcher's extended holomorphic anomaly equation.

In this paper, on Riemannian manifolds with boundary, we establish a Yau type gradient estimate and Liouville theorem for harmonic functions under Dirichlet boundary condition. Under a similar setting, we also formulate a Souplet-Zhang type…

Considering some parameters and by means of an inequality of Hadamard, we derive general half-discrete Hilbert-type inequalities. Then we highlight some special cases.

We address a linearity problem for differentiable vectors in representations of infinite-dimensional Lie groups on locally convex spaces, which is similar to the linearity problem for the directional derivatives of functions.

We defined generalized \delta-derivations of algebra A as linear mapping \chi associated with usual \delta-derivation \phi by the rule \chi(xy)=\delta(\chi(x)y+x\phi(y))=\delta(\phi(x)y+x\chi(y)) for any x,y \in A. We described generalized…

Different symmetry formalisms for difference equations on lattices are reviewed and applied to perform symmetry reduction for both linear and nonlinear partial difference equations. Both Lie point symmetries and generalized symmetries are…

We consider the linear heat equation on a bounded domain. We study estimates of the derivatives, up to the second order, of the solution locally in time in the Lebesgue spaces. We give a self-contained proof of the estimates in the…

We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by improvements of Young's inequality. We also give a generalized Han's inequality.

The purpose of this paper is to generalize the self-duality equation by Tchrakian and Corrigan et. al.. Novel generalized self-duality equations on higher-dimensional spaces are discussed. This class of equations includes the usual…

In this article we give, for the fist time the solution of the general difference equation of 2-degree. We also give as application the expansion of a continued fraction into series, which was first proved, found in the past by the author.

In this paper, motivated by the work of Qi S. Zhang in [28], we derive Li-Yau gradient bounds for positive solutions of the f-heat equation on closed manifolds with Bakry-Emery Ricci curvature bounded below.

We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.

In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…

Since Li and Yau obtained the gradient estimate for the heat equation, related estimates have been extensively studied. With additional curvature assumptions, matrix estimates that generalize such estimates have been discovered for various…

We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which…

The very few 5-th order differential equations which have 4-th order Calabi-Yau equations as pullbacks are listed. We use the pullback of Yifan Yang that in most cases has much lower degree than the usual pullback.

We study the elliptic version of doubly nonlinear diffusion equations on a complete Riemannian manifold $(M,g)$. Through the combination of a special nonlinear transformation and the standard Nash-Moser iteration procedure, some Cheng-Yau…