1,068 research outputs found
Shape optimization for monge-ampére equations via domain derivative
In this note we prove that, if Ω is a smooth, strictly convex, open set in R n (n ≥ 2) with given measure, the L 1 norm of the convex solution to the Dirichlet problem detD 2u = 1 in , u = 0 on δΩ, is minimum whenever is an ellipsoid
Singular anisotropic elliptic equations with gradient-dependent lower order terms
We prove the existence of a solution to a singular anisotropic elliptic
equation in a bounded open subset of with ,
subject to a homogeneous boundary condition: \begin{equation} \label{eq0}
\left\{ \begin{array}{ll} \mathcal A u+ \Phi(u,\nabla u)=\Psi(u,\nabla u)+
\mathfrak{B} u \quad& \mbox{in } \Omega,\\ u=0 & \mbox{on } \partial\Omega.
\end{array} \right. \end{equation} Here is the anisotropic
-Laplace operator, while is an operator from
into
satisfying suitable, but general, structural assumptions. and are
gradient-dependent nonlinearities whose models are the following:
\begin{equation*} \label{phi}\Phi(u,\nabla u):=\left(\sum_{j=1}^N
\mathfrak{a}_j |\partial_j u|^{p_j}+1\right)|u|^{m-2}u, \quad \Psi(u,\nabla
u):=\frac{1}{u}\sum_{j=1}^N |u|^{\theta_j} |\partial_j u|^{q_j}.
\end{equation*} We suppose throughout that, for every ,
\begin{equation*}\label{ass} \mathfrak{a}_j\geq 0, \quad \theta_j>0, \quad
0\leq q_j<p_j, \quad 1<p_j,m\quad \mbox{and}\quad p<N, \end{equation*} and we
distinguish two cases: 1) for every , we have ;
2) there exists such that . In this last situation,
we look for non-negative solutions of \eqref{eq0}
Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Ampère type
The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow
Symmetry breaking in a constrained cheeger type isoperimetric inequality
The study of the optimal constant Kq(Ω) in the Sobolev inequality ∥u∥Lq(Ω) ≤ 1/Kq(Ω)∥Du∥(double-struck Rn), 1 ≤ q < 1∗, for BV functions which are zero outside Ω and with zero mean value inside Ω, leads to the definition of a Cheeger type constant. We are interested in finding the best possible embedding constant in terms of the measure of Ω alone. We set up an optimal shape problem and we completely characterize, on varying the exponent q, the behaviour of optimal domains. Among other things we establish the existence of a threshold value 1 ≤ q < 1∗ above which the symmetry of optimal domains is broken. Several differences between the cases n = 2 and n ≥ 3 are emphasized
Existence of minimizers for eigenvalues of the Dirichlet-Laplacian with a drift
This paper deals with the eigenvalue problem for the operator L=-δ-x{dot operator}∇ with Dirichlet boundary conditions. We are interested in proving the existence of a set minimizing any eigenvalue λk of L under a suitable measure constraint suggested by the structure of the operator. More precisely we prove that for any c>0 and k∈N the following minimization problemmin<>{λk(Ω):Ωquasi-openset,∫Ωe|x|2/2dx≤c} has a solution
49Cr: Towards full spectroscopy up to 4 MeV
The nucleus 49Cr has been studied analysing gamma-gamma coincidences in the
reaction 46Ti(alpha,n)49Cr at the bombarding energy of 12 MeV. The level scheme
has been greatly extended at low excitation energy and several new lifetimes
have been determined by means of the Doppler Shift Attenuation Method.
Shell model calculations in the full pf configuration space reproduce well
negative-parity levels. Satisfactory agreement is obtained for positive parity
levels by extending the configuration space to include a nucleon-hole either in
the 1d3/2 or in the 2s1/2 orbitals.
A nearly one-to-one correspondence is found between experimental and
theoretical levels up to an excitation energy of 4 MeV.
Experimental data and shell model calculations are interpreted in terms of
the Nilsson diagram and the particle-rotor model, showing the strongly coupled
nature of the bands in this prolate nucleus. Nine values of K(pi) are proposed
for the levels observed in this experiment.
As a by-result it is shown that the values of the experimental magnetic
moments in 1f7/2 nuclei are well reproduced without quenching the nucleon
g-factors.Comment: 13 pages, 8 figure
Differences in Perceptions of the Housing Cost Burden Among European Countries
In this article we perform a comparative analysis of the self-reported perception of the housing cost burden as an indicator of potential financial distress. We employ EU-SILC data on five European countries – France, Germany, Italy, Spain and the UK – for years from 2005 to 2010. Wide differences emerge between Germany, France and the UK on the one hand, and Italy and Spain on the other. Estimation of the housing cost burden by means of logit models allows us to relate the probability of a high burden to both micro and macro-economic variables and to identify differences among countries. As for socio-economic variables, our results reveal the existence of life-cycle effects and a lower burden for homeowners. As for aggregate variables, GDP growth and higher consumer confidence contribute to reducing the probability of a high burden, whereas high levels of unemployment and inequality contribute to increase it. At country level, we observe differences in the size of the impact of the explanatory variables on the probability of perceiving a high burden, especially for covariates such as age, homeownership status and education
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