Related papers: On the anisotropic Kirchhoff-Plateau problem
In this short paper we prove a global logarithmic stability of the Cauchy problem for H 2-solutions of an anisotropic elliptic equation in a Lip-schitz domain. The result we obtained is based on tools borrowed from the existing technics to…
In this paper, we consider solutions to the following fourth order anisotropic nonlinear Schr\"odinger equation in $\R \times \R^2$, $$ \left\{ \begin{aligned} &\textnormal{i}\partial_t\psi+\partial_{xx} \psi-\partial_{yyyy} \psi…
We study conditions of reduction of the multidimensional wave equation - a system of the d'Alembert and Hamilton equations. We prove necessary conditions for compatibility of such system of the reduction conditions. Possible types of the…
In this paper, we consider the Minkowski problem associated with the solution to the anisotropic $p$-Laplacian (or Finsler $p$-Laplacian) equation, namely, the Minkowski problem of anisotropic $p$-torsional rigidity. The sufficient and…
In this paper we investigate a class of elliptic problems involving a nonlocal Kirchhoff type operator with variable coefficients and data changing its sign. Under appropriated conditions on the coefficients, we have shown existence and…
We discuss the solvability of a parameter dependent cantilever-type boundary value problem. We provide an existence and localization result for the positive solutions via a Birkhoff-Kellogg type theorem. We also obtain, under additional…
Solving the Plateau problem means to find the surface with minimal area among all surfaces with a given boundary. Part of the problem actually consists of giving a suitable definition to the notions of 'surface', 'area' and 'boundary'. In…
Two distinct non-singular interior models that describe anisotropic spherical configurations are presented in this work. We develop the Einstein field equations and the associated mass function in accordance with a static spherical…
We discuss the leading order of anisotropic hydrodynamics expansion. It has already been shown that in the (0+1) and (1+1)-dimensional cases it is consistent with the second order viscous hydrodynamics, and it provides a striking agreement…
In this work, we present a class of relativistic and well-behaved solution to Einstein's field equations for anisotropic matter distribution. We perform our analysis by using the Buchdahl ansatz for the metric function grr. Three different…
In this paper we present a very simple proof of the existence of at least one non trivial solution for a Kirchhoff type equation on $\RN$, for $N\ge 3$. In particular, in the first part of the paper we are interested in studying the…
In this paper we show that any static and spherically symmetric anisotropic solution of the Einstein field equations can be thought as a system sourced by certain deformed isotropic system in the context of Minimal Geometric…
We consider the Gelfand problem on a planar domain. Under some conditions on the potential, we provide the first examples of multiplicity for blowing-up solutions at a given point in the domain. The argument is based on a refined…
We show uniqueness results for the anisotropic Calder\'{o}n problem stated on transversally anisotropic manifolds. Moreover, we give a convexity result for the range of Dirichlet-to-Neumann maps on general Riemannian manifolds near the zero…
In this paper, after reviewing the form of the constitutive equations for a third grade Korteweg fluid, recently derived by means of an extended Liu procedure, an equilibrium problem is investigated. By considering a two--dimensional…
A rigorous derivation of point vortex systems from kinetic equations has been a challenging open problem, due to singular layers in the inviscid limit, giving a large velocity gradient in the Boltzmann equations. In this paper, we derive…
We consider Kasner space-time describing anisotropic three dimensional expansion of the fluid and obtain the dissipative evolution equations for shear stress tensor and energy density from kinetic theory. For this, we use the iterative…
We highlight some recent new delevelopments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in isotropic Sobolev or Besov scales. Specifically, we focus…
We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have…
We consider mildly degenerate Kirchhoff equations with a small parameter and a weak dissipation term. We prove the existence of global solutions when the parameter is small with respect to the size of initial data. Then we provide…