Generalized solutions for the mean curvature equation
نویسندگان
چکیده
منابع مشابه
Solutions to the mean curvature equation by fixed point methods
We give conditions on the boundary data, in order to obtain at least one solution for the problem (1) below, withH a smooth function. Our motivation is a better understanding of the Plateau’s problem for the prescribed mean curvature equation.
متن کاملA comparison result for radial solutions of the mean curvature equation
We establish two comparison results between the solutions of a class of mean curvature equations and pieces of arcs of circles that satisfy the same Neumann boundary condition. Finally we present a number of examples where our estimates can be applied, some of them have a physical motivation.
متن کاملExistence and Regularity of Weak Solutions to the Prescribed Mean Curvature Equation for a Nonparametric Surface
It is known that for the parametric Plateau’s problem, weak solutions can be obtained as critical points of a functional (see [2, 6, 7, 8, 10, 11]). The nonparametric case has been studied for H = H(x,y) (and generally H = H(x1, . . . ,xn) for hypersurfaces in Rn+1) by Gilbarg, Trudinger, Simon, and Serrin, among other authors. It has been proved [5] that there exists a solution for any smooth ...
متن کاملExact Solutions of the Generalized Kuramoto-Sivashinsky Equation
In this paper we obtain exact solutions of the generalized Kuramoto-Sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems. The methods used to determine the exact solutions of the underlying equation are the Lie group analysis and the simplest equation method. The solutions obtained are then plotted.
متن کاملSubharmonic solutions of the prescribed curvature equation∗
We study the existence of subharmonic solutions of the prescribed curvature equation − ( u′/ √ 1 + u′ )′ = f(t, u). According to the behaviour at zero, or at infinity, of the prescribed curvature f , we prove the existence of arbitrarily small classical subharmonic solutions, or bounded variation subharmonic solutions with arbitrarily large oscillations. 2010 Mathematics Subject Classification:...
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: Pacific Journal of Mathematics
سال: 1980
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1980.88.297