We show that the fundamental tone of the bilaplacian with Dirichlet or Navier boundary conditions on radially symmetric domains is always simple in dimension $N\ge3$. In dimension $N=2$ we show that it is simple if the inner radius is big enough.
We give a short and self-contained proof of the interior $\mathcal C^{1,1}$ regularity of solutions $\varphi:Ω\to \mathbb{R}$ to the eikonal equation $|\nabla \varphi|=1$ in an open set $Ω\subset \mathbb{R}^{N}$ in dimension $N\geq 1$ under the assumption that $\varphi$ is pointwise differentiable in $Ω$.
We prove two forms of uncertainty principle for the Schrödinger group generated by the Ornstein-Uhlenbeck operator. As a consequence, we derive a related (in fact, equivalent) result for the imaginary harmonic oscillator.
Strong unique continuation properties and a classification of the asymptotic profiles are established for the fractional powers of a Schrödinger operator with a Hardy-type potential, by means of an Almgren monotonicity formula combined with a blow-up analysis.
In this paper we prove that the only blowup solutions to the focusing, quintic nonlinear Schr{ö}dinger equation with mass equal to the mass of the soliton are rescaled solitons or the pseudoconformal transformation of those solitons.
Boundary value problems for non-linear parabolic equations with singular potentials are considered. Existence and non-existence results as an application of different Hardy inequalities are proved. Blow-up conditions are investigated too.
Communicating cultural heritage to the public has gained popularity in many African countries and the world at large. However,little efforts have been done to promote the practice of public archaeology in Tanzania. The main reason is the dominance of conventional archaeology which is mainly meant for academic consumption. In this kind of practice, the participation of local communities has been passive. This paper explores local communities’ understanding of cultural heritage resources focusing on local communities in the Mtwara Region of Tanzania. The results of this study reveal that little effort has been made by archaeologists and cultural heritage professionals to create awareness among local communities on matters related to archaeology and cultural heritage resources. Apart from discussing the state of local communities’ awareness on archaeology and cultural heritage resources, the paper also discusses the importance of communicating cultural heritage resources to the general public and the need to engage local communities in the conservation and preservation of cultural heritage resources.
We study the boundary behaviors of a complete conformal metric which solves the $σ_k$-Ricci problem on the interior of a manifold with boundary. We establish asymptotic expansions and also $C^1$ and $C^2$ estimates for this metric multiplied by the square of the distance in a small neighborhood of the boundary.
For the non cutoff radially symmetric homogeneous Boltzmann equation with Maxwellian molecules, we give the numerical solutions using symbolic manipulations and spectral decomposition of Hermit functions. The initial data can belong to some measure space.
We provide a counterexample of Wente's inequality in the context of Neumann boundary conditions. We will also show that Wente's estimates fails for general boundary conditions of Robin type.
Free bondary value problem for elliptic differential-operator equations with variable coefficients is studied. The uniform maximal regularity properties and Fredholmness of this problem are obtained in vector-valued Holder spaces.
We consider entire solutions $u$ to the minimal surface equation in $R^N$, with $ N\ge8,$ and we prove the following sharp result : if $N-7$ partial derivatives $ \frac{\partial u }{\partial {x_j}}$ are bounded on one side (not necessarily the same), then $u$ is necessarily an affine function.
The paper is concerned with the regularity of weak solutions to the Navier-Stokes equations. The aim is to investigate on a relaxed Prodi-Serrin condition in order to obtain regularity for t > 0. The most interesting aspect of the result is that no compatibility condition is required to the initial data $v_0\in J^2(\OO) J2(Ω)$.
S. Heinemeyer, J. Hernandez-Garcia, M. J. Herrero
et al.
We study the radiative corrections to the mass of the lightest Higgs boson of the MSSM from three generations of Majorana neutrinos and sneutrinos. The spectrum of the MSSM is augmented by three right handed neutrinos and their supersymmetric partners. A seesaw mechanism of type I is used to generate the physical neutrino masses and oscillations that we require to be in agreement with present neutrino data. We present a full one-loop computation of these Higgs mass corrections and analyze in full detail their numerical size in terms of both the MSSM and the new (s)neutrino parameters. A critical discussion on the different possible renormalization schemes and their implications, in particular concerning decoupling, is included.
In this paper we consider self-similar blow-up solutions for the generalized deterministic KPZ~equation $u_t = u_{xx} + λ\vert u_x \vert ^q, λ> 0, q > 2.$ The asymptotic behavior of self-similar solutions are studied.
Let $p\in(1,n)$. If $Ω$ is a convex domain in $\rn$ whose $p$-capacitary potential function $u$ is $(1-p)/(n-p)$-concave (i.e. $u^{(1-p)/(n-p)}$ is convex), then $Ω$ is a ball.
In this paper, we study the initial boundary value problem for the two dimensional strong damped wave equation with exponentially growing source and damping terms. We first show the well-posedness of this problem and then prove the existence of the global attractor in $(H_{0}^{1}(Ω)\cap L^{\infty}(Ω))\times L^{2}(Ω)$.
We consider Monge-Ampere equations with bounded right hand side and we study the geometric properties of sections centered at a boundary point. We prove that under natural boundary conditions such sections are equivalent to ellipsoids.
In this work a class of self-adjoint quasilinear third-order evolution equations is determined. Some conservation laws of them are established and a generalization on a self-adjoint class of fourth-order evolution equations is presented.