197 research outputs found
Overdetermined boundary value problems for the -Laplacian
We consider overdetermined boundary value problems for the -Laplacian
in a domain of and discuss what kind of implications on the
geometry of the existence of a solution may have. The classical
-Laplacian, the normalized or game-theoretic -Laplacian and the
limit of the -Laplacian as are considered and provide
different answers.Comment: 9 pages, 1 figur
Minimal resistance of curves under the single impact assumption
We consider the hollow on the half-plane defined by a function , , and a vertical flow of point particles incident on the hollow. It is assumed that satisfies the so-called single impact condition (SIC): each incident particle is elastically reflected by graph and goes away without hitting the graph of anymore. We solve the problem: find the function minimizing the force of resistance created by the flow. We show that the graph of the minimizer is formed by two arcs of parabolas symmetric to each other with respect to the -axis. Assuming that the resistance of equals 1, we show that the minimal resistance equals . This result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014), pp. 2730--2742] stating in particular that the minimal resistance of a hollow in higher dimensions equals 0.5. We additionally consider a similar problem of minimal resistance, where the hollow in the half-space is defined by a radial function satisfying the SIC, , with , for , and for , and the flow is parallel to the -axis. The minimal resistance is greater than 0.5 (and coincides with 0.6435 when d = 1) and converges to 0.5 as
Pflanzenvergiftungen — psychiatrische Aspekte
Zusammenfassung: Seit der Antike sind Pflanzenvergiftungen dokumentiert, trotzdem werden Intoxikationen mit pflanzlichen Giften im psychiatrischen Schrifttum wenig beachtet, und die Gefahr durch Giftpflanzen wird gemeinhin verkannt. In diesem Artikel wird diese Problematik erörtert. Es werden weiterhin entsprechende Empfehlungen zur Vermeidung von Pflanzenvergiftungen und zum allgemeinen Umgang mit deren Folgen gegebe
Examination of the effect of acute levodopa administration on the loudness dependence of auditory evoked potentials (LDAEP) in humans
Rationale: The loudness dependence of the auditory evoked potential (LDAEP) is considered a noninvasive in vivo marker of central serotonergic functioning in humans. Nevertheless, results of genetic association studies point towards a modulation of this biomarker by dopaminergic neurotransmission. Objective: We examined the effect of dopaminergic modulation on the LDAEP using L-3,4-dihydroxyphenylalanine (levodopa)/benserazide (Madopar®) as a challenge agent in healthy volunteers. Methods: A double-blind placebo-controlled challenge design was chosen. Forty-two healthy participants (21 females and 21 males) underwent two LDAEP measurements, following a baseline LDAEP measurement either placebo or levodopa (levodopa 200mg/benserazide 50mg) were given orally. Changes in the amplitude and dipole source activity of the N1/P2 intensities (60, 70, 80, 90, and 100dB) were analyzed. Results: The participants of neither the levodopa nor the placebo group showed any significant LDAEP alterations compared to the baseline measurement. The test-retest reliability (Cronbachs Alpha) between baseline and intervention was 0.966 in the verum group and 0.759 in the placebo group, respectively. Conclusions: The administration of levodopa showed no effect on the LDAEP. These findings are in line with other trials using dopamine receptor agonist
Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions
We introduce an iterative method for computing the first eigenpair
for the -Laplacian operator with homogeneous Dirichlet
data as the limit of as , where
is the positive solution of the sublinear Lane-Emden equation
with same boundary data. The method is
shown to work for any smooth, bounded domain. Solutions to the Lane-Emden
problem are obtained through inverse iteration of a super-solution which is
derived from the solution to the torsional creep problem. Convergence of
to is in the -norm and the rate of convergence of
to is at least . Numerical evidence is
presented.Comment: Section 5 was rewritten. Jed Brown was added as autho
On a classical spectral optimization problem in linear elasticity
We consider a classical shape optimization problem for the eigenvalues of
elliptic operators with homogeneous boundary conditions on domains in the
-dimensional Euclidean space. We survey recent results concerning the
analytic dependence of the elementary symmetric functions of the eigenvalues
upon domain perturbation and the role of balls as critical points of such
functions subject to volume constraint. Our discussion concerns Dirichlet and
buckling-type problems for polyharmonic operators, the Neumann and the
intermediate problems for the biharmonic operator, the Lam\'{e} and the
Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape
Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27
September 201
Self-similarity and long-time behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source
This paper deals with the long-time behavior of solutions of nonlinear
reaction-diffusion equations describing formation of morphogen gradients, the
concentration fields of molecules acting as spatial regulators of cell
differentiation in developing tissues. For the considered class of models, we
establish existence of a new type of ultra-singular self-similar solutions.
These solutions arise as limits of the solutions of the initial value problem
with zero initial data and infinitely strong source at the boundary. We prove
existence and uniqueness of such solutions in the suitable weighted energy
spaces. Moreover, we prove that the obtained self-similar solutions are the
long-time limits of the solutions of the initial value problem with zero
initial data and a time-independent boundary source
Phase field approach to optimal packing problems and related Cheeger clusters
In a fixed domain of we study the asymptotic behaviour of optimal
clusters associated to -Cheeger constants and natural energies like the
sum or maximum: we prove that, as the parameter converges to the
"critical" value , optimal Cheeger clusters
converge to solutions of different packing problems for balls, depending on the
energy under consideration. As well, we propose an efficient phase field
approach based on a multiphase Gamma convergence result of Modica-Mortola type,
in order to compute -Cheeger constants, optimal clusters and, as a
consequence of the asymptotic result, optimal packings. Numerical experiments
are carried over in two and three space dimensions
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