Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Barbatis, Gerassimos"'
There are two Rellich inequalities for the bilaplacian, that is for $\int (\Delta u)^2dx$, the one involving $|\nabla u|$ and the other involving $|u|$ at the RHS. In this article we consider these inequalities with sharp constants and obtain sharp S
Externí odkaz:
http://arxiv.org/abs/2312.00433
Autor:
Barbatis, Gerassimos
We present a review of results that have been obtained in the past twenty-five years concerning the $L^p$-Hardy inequality with distance to the boundary. We concentrate on results where the best Hardy constant is either computed exactly or estimated
Externí odkaz:
http://arxiv.org/abs/2311.08017
Let $\Omega$ be a bounded domain in $\mathbb{R}^N$ with $C^2$ boundary and let $K\subset\partial\Omega$ be either a $C^2$ submanifold of the boundary of codimension $k
Externí odkaz:
http://arxiv.org/abs/2207.04667
We study Rellich inequalities associated to higher-order elliptic operators in the Euclidean space. The inequalities are expressed in terms of an associated Finsler metric. In the case of half-spaces we obtain the sharp constant while for a general c
Externí odkaz:
http://arxiv.org/abs/2102.08309
We obtain heat kernel estimates for a class of fourth order non-uniformly elliptic operators in two dimensions. Contrary to existing results, the operators considered have symbols that are not strongly convex. This rises certain difficulties as it is
Externí odkaz:
http://arxiv.org/abs/2012.03615
Publikováno v:
Bulletin of the Hellenic Mathematical Society, Volume 63 (2019), pp 64-96
In this article we compute the best Sobolev constants for various Hardy-Sobolev inequalities with sharp Hardy term. This is carried out in three different environments: interior point singularity in Euclidean space, interior point singularity in hype
Externí odkaz:
http://arxiv.org/abs/1909.10212
We consider a class of fourth order uniformly elliptic operators in planar Euclidean domains and study the associated heat kernel. For operators with $L^{\infty}$ coefficients we obtain Gaussian estimates with best constants, while for operators with
Externí odkaz:
http://arxiv.org/abs/1712.02963
We study the Hardy inequality when the singularity is placed on the boundary of a bounded domain in $\mathbb{R}^n$ that satisfies both an interior and exterior ball condition at the singularity. We obtain the sharp Hardy constant $n^2/4$ in case the
Externí odkaz:
http://arxiv.org/abs/1701.06336
Gaussian estimates with best constants for higher-order Schr\'odinger operators with Kato potentials
Autor:
Barbatis, Gerassimos
We establish Gaussian estimates on the heat kernel of a higher-order uniformly elliptic Schr\"odinger operator with variable highest order coefficients and with a Kato class potential. The estimates involve the sharp constant in the Gaussian exponent
Externí odkaz:
http://arxiv.org/abs/1511.08711
We consider the $L^p$ Hardy inequality involving the distance to the boundary for a domain in the $n$-dimensional Euclidean space. We study the dependence on $p$ of the corresponding best constant and we prove monotonicity, continuity and differentia
Externí odkaz:
http://arxiv.org/abs/1509.09107