Nikos Labropoulos
Sharp Nash Inequalities on the unit sphere. The influence of symmetries.
Fri, 01/15/2010 - 16:01 — SomNambulAuthors: Athanase Cotsiolis, Nikos Labropoulos
Subjects: Functional Analysis
AbstractIn this paper both we establish the best constants for the Nash inequalities
on the standard unit sphere $\mathbb{S}^n$ of $\mathbb{R}^{n+1}$ and we give
answers on the existence of extremal functions on the corresponding problems.
Also we study the problem of the best constants in the case, where the data are
invariant under the action of the group $G=O(k)\times O(m)$, and we find the
best constants.Sharp Nash inequalities on manifolds with boundary in the presence of symmetries.
Mon, 12/21/2009 - 16:01 — SomNambulAuthors: Athanase Cotsiolis, Nikos Labropoulos
Subjects: Functional Analysis
AbstractIn this paper we establish the best constant $\widetilde
A_{opt}(\overline{M})$ for the Trace Nash inequality on a $n-$dimensional
compact Riemannian manifold in the presence of symmetries, which is an
improvement over the classical case due to the symmetries which arise and
reflect the geometry of manifold. This is particularly true when the data of
the problem is invariant under the action of an arbitrary compact subgroup $G$
of the isometry group $Is(M,g)$, where all the orbits have infinite cardinal.Exponential elliptic boundary value problems on a solid torus in the critical of supercritical case.
Mon, 12/21/2009 - 16:01 — SomNambulAuthors: Athanase Cotsiolis, Nikos Labropoulos
Subjects: Analysis of PDEs
AbstractIn this paper we investigate the behavior and the existence of positive and
non-radially symmetric solutions to nonlinear exponential elliptic model
problems defined on a solid torus $\bar{T}$ of $\mathbb{R}^3$, when data are
invariant under the group $G=O(2)\times I \subset O(3)$. The model problems of
interest are stated below: ${ll} {\bf(P_1)} & \displaystyle
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