Examples of discontinuous, divergence-free solutions to elliptic variational problems
نویسندگان
چکیده
We give an example of a bounded discontinuous divergence-free solution of a linear elliptic system with measurable bounded coefficients in R and a corresponding example for a Stokes-like system.
منابع مشابه
Discontinuous Galerkin Methods for Solving Elliptic Variational Inequalities
We study discontinuous Galerkin methods for solving elliptic variational inequalities, of both the first and second kinds. Analysis of numerous discontinuous Galerkin schemes for elliptic boundary value problems is extended to the variational inequalities. We establish a priori error estimates for the discontinuous Galerkin methods, which reach optimal order for linear elements. Results from so...
متن کاملDiscontinuous Solutions of Linear, Degenerate Elliptic Equations
We give examples of discontinuous solutions of linear, degenerate elliptic equations with divergence structure. These solve positively conjectures of De Giorgi.
متن کاملExistence of at least three weak solutions for a quasilinear elliptic system
In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...
متن کاملOn Divergence-free Drifts
We investigate the validity and failure of Liouville theorems and Harnack inequalities for parabolic and elliptic operators with low regularity coefficients. We are particularly interested in operators of the form ∂t−∆+ b ·∇ resp. −∆+ b ·∇ with a divergence-free drift b. We prove the Liouville theorem and Harnack inequality when b ∈ L∞(BMO) resp. b ∈ BMO−1 and provide a counterexample demonstra...
متن کامل. A P ] 1 5 M ar 2 00 6 Conservation laws for conformal invariant variational problems
We succeed in writing 2-dimensional conformally invariant nonlinear elliptic PDE (harmonic map equation, prescribed mean curvature equations...etc) in divergence form. This divergence free quantities generalize to target manifolds without symmetries the well known conservation laws for harmonic maps into homogeneous spaces. From this form we can recover, without the use of moving frame, all the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010