Search results for " Elliptic"

Steady‐state solutions of the aerotaxis problem

2022

We study the steady-state system of aerotaxis equations in higher dimensions.It is shown that the existence and multiplicity of solutions depend on the totalmass of the colony of bacteria, the energy function, and the boundary conditions.

On the solutions to 1-Laplacian equation with L1 data

2009

AbstractIn the present paper we study the behaviour, as p goes to 1, of the renormalized solutions to the problems(0.1){−div(|∇up|p−2∇up)=finΩ,up=0on∂Ω, where p>1, Ω is a bounded open set of RN (N⩾2) with Lipschitz boundary and f belongs to L1(Ω). We prove that these renormalized solutions pointwise converge, up to “subsequences,” to a function u. With a suitable definition of solution we also prove that u is a solution to a “limit problem.” Moreover we analyze the situation occurring when more regular data f are considered.

Asymptotic behaviors of solutions to quasilinear elliptic equations with Hardy potential

2016

Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations −Δpu − μ |x| p |u| p−2 u + m|u| p−2 u = f(u), x ∈ RN , where 1 0 and f is a continuous function. peerReviewed

BCG Mass Evolution in Cosmological Hydro-Simulations

2018

We analyze the stellar growth of Brightest Cluster Galaxies (BCGs) produced by cosmological zoom-in hydrodynamical simulations of the formation of massive galaxy clusters. The evolution of the stellar mass content is studied considering different apertures, and tracking backwards either the main progenitor of the $z=0$ BCG or that of the cluster hosting the BCG at $z=0$. Both methods lead to similar results up to $z \simeq 1.5$. The simulated BCGs masses at $z=0$ are in agreement with recent observations. In the redshift interval from $z=1$ to $z=0$ we find growth factors 1.3, 1.6 and 3.6 for stellar masses within 30kpc, 50kpc and 10% of $R_{500}$ respectively. The first two factors, and in…

Geological modeling of Altavilla Milicia (Sicily) using HVSR data

2014

At today the use of inversion of HVSR curves is mainly limited to derive average parameters of the shear wave velocity, although recently they have been used also for a detailed reconstruction of the roof of the seismic bedrock (Di Stefano et al. 2014). Since ambient vibrations may contain waves travelling in all directions, as body waves and Rayleigh and Love waves, a limit of this method lies in the uncertain composition of seismic noise, in the lack of knowledge about the microseismic field and in the subjective choices regarding the data processing. This work aims to verify the potential and limits of the HVSR inversion for the purposes of geological reconstruction of the subsoil in hea…

Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources

2018

In this paper we construct a viscosity solution of a two-phase free boundary problem for a class of fully nonlinear equation with distributed sources, via an adaptation of the Perron method. Our results extend those in [Caffarelli, 1988], [Wang, 2003] for the homogeneous case, and of [De Silva, Ferrari, Salsa, 2015] for divergence form operators with right hand side.

Global properties of generalized Ornstein–Uhlenbeck operators on Lp(RN,RN) with more than linearly growing coefficients

2009

AbstractWe show that the realization Ap of the elliptic operator Au=div(Q∇u)+F⋅∇u+Vu in Lp(RN,RN), p∈[1,+∞[, generates a strongly continuous semigroup, and we determine its domain D(Ap)={u∈W2,p(RN,RN):F⋅∇u+Vu∈Lp(RN,RN)} if 1<p<+∞. The diffusion coefficients Q=(qij) are uniformly elliptic and bounded together with their first-order derivatives, the drift coefficients F can grow as |x|log|x|, and V can grow logarithmically. Our approach relies on the Monniaux–Prüss theorem on the sum of noncommuting operators. We also prove Lp–Lq estimates and, under somewhat stronger assumptions, we establish pointwise gradient estimates and smoothing of the semigroup in the spaces Wα,p(RN,RN), α∈[0,1], wher…

Existence and multiplicity results for semilinear elliptic Dirichlet problems in exterior domains

1995

A Viscosity Equation for Minimizers of a Class of Very Degenerate Elliptic Functionals

2013

We consider the functional $$J(v) = \int_\varOmega\bigl[f\bigl(|\nabla v|\bigr) - v\bigr] dx, $$ where Ω is a bounded domain and f:[0,+∞)→ℝ is a convex function vanishing for s∈[0,σ], with σ>0. We prove that a minimizer u of J satisfies an equation of the form $$\min\bigl(F\bigl(\nabla u, D^2 u\bigr), |\nabla u|-\sigma\bigr)=0 $$ in the viscosity sense.

Location of solutions for quasi-linear elliptic equations with general gradient dependence

2017

Existence and location of solutions to a Dirichlet problem driven by $(p,q)$-Laplacian and containing a (convection) term fully depending on the solution and its gradient are established through the method of subsolution-supersolution. Here we substantially improve the growth condition used in preceding works. The abstract theorem is applied to get a new result for existence of positive solutions with a priori estimates.