2,850 research outputs found
A stability result for nonlinear Neumann problems under boundary variations
In this paper we study, in dimension two, the stability of the solutions of
some nonlinear elliptic equations with Neumann boundary conditions, under
perturbations of the domains in the Hausdorff complementary topology.Comment: 26 page
Local density of Caputo-stationary functions in the space of smooth functions
We consider the Caputo fractional derivative and say that a function is
Caputo-stationary if its Caputo derivative is zero. We then prove that any
function can be approximated in by a a function
that is Caputo-stationary in , with initial point . Otherwise said,
Caputo-stationary functions are dense in .Comment: 19 pages, 4 figure
On the honeycomb conjecture for Robin Laplacian eigenvalues
We prove that the optimal cluster problem for the sum of the first Robin
eigenvalue of the Laplacian, in the limit of a large number of convex cells, is
asymptotically solved by (the Cheeger sets of) the honeycomb of regular
hexagons. The same result is established for the Robin torsional rigidity
On the characterization of the compact embedding of Sobolev spaces
For every positive regular Borel measure, possibly infinite valued, vanishing
on all sets of -capacity zero, we characterize the compactness of the
embedding W^{1,p}({\bf R}^N)\cap L^p ({\bf R}^N,\mu)\hr L^q({\bf R}^N) in
terms of the qualitative behavior of some characteristic PDE. This question is
related to the well posedness of a class of geometric inequalities involving
the torsional rigidity and the spectrum of the Dirichlet Laplacian introduced
by Polya and Szeg\"o in 1951. In particular, we prove that finite torsional
rigidity of an arbitrary domain (possibly with infinite measure), implies the
compactness of the resolvent of the Laplacian.Comment: 19 page
Non Linear System for a Veritable PID Substitute
The paper deals with a non-linear system largely used in biology, which, in
certain conditions and for particular coefficient values, becomes linear, with
a linear diagram over a large range of time. It can be used as a veritable
regulator in systems' controlComment: 4 pages, exposed on 2nd "European Conference on Computer Sience and
Applications" - XA2008, Timisoara, Romani
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