A minimization problem with free boundary related to a cooperative system
نویسندگان
چکیده
منابع مشابه
A two-phase free boundary problem for a semilinear elliptic equation
In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...
متن کاملA free boundary problem with curvature
In this paper we are interested in a free boundary problem whith a motion law involving the mean curvature term of the free boundary. Viscosity solutions are introduced as a notion of global-time solutions past singularities. We show the comparison principle for viscosity solutions, which yields the existence of minimal and maximal solutions for given initial data. We also prove uniqueness of t...
متن کاملTHE STEFAN PROBLEM WITH KINETIC FUNCTIONS AT THE FREE BOUNDARY
This paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. A model problem with nonlinear kinetic law is considered. The main result is an existence theorem. The mathematical effects of the kinetic term are discussed
متن کاملA Two-phase Problem with a Lower-dimensional Free Boundary
For a bounded domain D ⊂ Rn, we study minimizers of the energy functional ∫ D |∇u| dx+ ∫ D∩(Rn−1×{0}) λχ{u>0} + λ χ{u<0} dHn−1, without any sign restriction on the function u. One of the main result states that the free boundaries Γ = ∂{u(·, 0) > 0} and Γ− = ∂{u(·, 0) < 0} never touch. Moreover, using Alexandrov-type reflection technique, we can show that in dimension n = 3 the free boundaries ...
متن کاملHomogenization of a Uid Problem with a Free Boundary
The stationary Stokes equations with a free boundary are studied in a perforated domain. The perforation consists of a periodic array of cylinders of size and distance O("). The free boundary is given as the graph of a function on a two-dimensional perforated domain. We derive equations for the two-scale limit of solutions. The limiting equation is a free boundary system. It involves a nonlinea...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2018
ISSN: 0012-7094
DOI: 10.1215/00127094-2018-0007