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The Harnack inequality and related properties for solutions to elliptic and parabolic equations with divergence-free lower-order coefficients
The Harnack inequality related properties elliptic
2010/11/15
We discuss the problem how "bad" may be lower-order coefficients in elliptic and parabolic second order equations to ensure some qualitative properties of solution such as strong maximum principle, H...
In this paper, we established a new Ostrowski-type inequality involving functions of two independent variables.
The optimal constant in the $L^2$ Folland-Stein inequality on the quaternionic Heisenberg group
Yamabe equation quaternionic contact structures
2010/12/7
We determine the best (optimal) constant in the L2 Folland-Stein inequality on the quaternionic Heisenberg group and the non-negative functions for which equality holds.
Log-Harnack Inequality for Stochastic Burgers Equations and Applications
stochastic Burgers equation log-Harnack inequality strong Feller property
2010/12/14
By proving an L2-gradient estimate for the corresponding Galerkin approximations,the log-Harnack inequality is established for the semigroup associated to a class of stochastic Burgers equations. As a...
Logarithmic Sobolev inequality for diffusion semigroups
Logarithmic Sobolev inequality Poincar´ e inequality Ornstein-Uhlenbeck semigroup
2010/12/8
Through the main example of the Ornstein-Uhlenbeck semigroup, the Bakry-Emery criterion is presented as a main tool to get functional inequalities as Poincar´e or logarithmic Sobolev inequalitie...
We propose a new variational problem which we call the Split Variational Inequality Problem (SVIP). It entails finding a solution of one Variational Inequality Problem (VIP), the image of which under ...
We establish the canonical class inequality for families of higher dimensional projective manifolds. As an application, we get a new inequality between the Chern numbers of 3-folds with smooth familie...
A Berezin-Li-Yau type inequality for the fractional Laplacian on a bounded domain
Berezin-Li-Yau type inequality fractional Laplacian bounded domain
2010/12/9
A Berezin-Li-Yau type inequality for (−) /2|, the fractional Laplacian op-erators restriced to a bounded domain ⊂ Rd for ∈ (0, 2], d ≥ 2, has not been known so far. First we positivel...
A volumetric Penrose inequality for conformally flat manifolds
volumetric Penrose inequality conformally flat manifolds
2010/12/1
We consider asymptotically flat Riemannian manifolds with nonnegative scalar curvature that are conformal to Rn \ , n 3, and so that their boundary is a minimal hypersurface.
Some improvements on the constants for the real Bohnenblust-Hille inequality
improvements constants real Bohnenblust-Hille inequality
2010/12/6
A classical inequality due to Bohnenblust and Hille states that for every N ∈ N and every m-linear mapping U : ℓN 1 × · · · × ℓN 1 → C we have N X i1,...,im=1 U(ei1 , ..., eim) 2m m...
A Note on the Paper $"$Poincaré Inequality on the Path Space of Poisson Point Processes"
Paper $"$Poincaré Inequality ath Space of Poisson Point Processes"
2010/12/1
In the recent paper [2] we proved a Poincar´e inequality on the path space of compound Poisson processes by using transition probabilities and the Markov property. Our purpose
is to develop a g...
On the Banach space valued Azuma inequality and small set isoperimetry of Alon-Roichman graphs
Banach space valued Azuma inequality small set isoperimetry of Alon-Roichman graphs
2010/12/14
We discuss the connection between the expansion of small sets in graphs, and the Schatten norms of their adjacency matrix. In conjunction with a variant of the Azuma inequality for uniformly smooth no...
On the constants in a Kato inequality for the Euler and Navier-Stokes equations
Navier-Stokes equations inequalities Sobolev spaces
2010/12/3
We continue an analysis, started in [10], of some issues related to the incompressible Euler or Navier-Stokes (NS) equations on a d-dimensional torus Td. More specifically, we consider the quadratic t...
An inequality for sums of binary digits, with application to Takagi functions
Takagi function Approximate convexity Digital sum inequality
2010/12/1
An inequality for sums of binary digits, with application to Takagi functions.
A weak Harnack inequality for fractional evolution equations with discontinuous coefficients
weak Harnack inequality Moser iterations fractional derivativ weak solutions
2010/12/13
We study linear time fractional diffusion equations in divergence form of time order less than one. It is merely assumed that the coefficients are measurable and bounded, and that they satisfy a unifo...