On uniqueness of entropy solutions for nonlinear elliptic degenerate anisotropic equations
Journal Title: Математичні Студії - Year 2017, Vol 47, Issue 1
Abstract
In the present paper we deal with the Dirichlet problem for a class of degenerate anisotropic elliptic second-order equations with L1-right-hand sides in a bounded domain of Rn (n⩾2). This class is described by the presence of a set of exponents q1,…,qn and a set of weighted functions ν1,…,νn in growth and coercitivity conditions on coefficients of the equations. The exponents qi characterize the rates of growth of the coefficients with respect to the corresponding derivatives of unknown function, and the functions νi characterize degeneration or singularity of the coefficients with respect to independent variables. Our aim is to study the uniqueness of entropy solution of the problem under consideration.
Authors and Affiliations
Yu. S. Gorban
Keywords
Related Articles
- EP ID EP310046
- DOI 10.15330/ms.47.1.59-70
- Views 60
- Downloads 0
Rings with the Kazimirsky condition and rings with projective socle
We construct the theory of diagonalizability for matrices over Bezout rings of stable range 1 with the Kazimirsky condition. It is shown that a ring of stable range 1 with the right (left) Kazimirsky condition is an elem...
The Cauchy problem with impulse action and degeneration for parabolic equations
We study the Cauchy problem for the second-order linear parabolic equations with impulse conditions in the time variable and power singularity in the coefficients of any order with respect to the time and space variables...
Existence of solitary traveling waves in Fermi-Pasta-Ulam system on 2D–lattice
The article deals with the Fermi–Pasta–Ulam system that describes an infinite system of particles on 2D–lattice. The main result concerns the existence of solitary traveling wave solutions. By means of critical point the...
Asymptotic properties of the impulse perturbation process under Levy approximation conditions with the point of equilibrium of the quality criterion
For the system of stochastic differential equations with Markov switchings and impulse disturbance in the conditions of Levy approximation in the conditions of a single point of equilibrium of the quality criterion, limi...
Distance between a maximum modulus point and zero set of an analytic function
Let f be an analytic function in the disk DR={z∈C:|z|≤R}, R∈(0,+∞]. We call a point w∈DR a maximum modulus point of f if |f(w)|=M(|w|,f), where M(r,f)=max{|f(z)|:|z|=r}. Denote by d(w,f) the distance between a maximum mo...