Entire solutions to equations of minimal surface type in six dimensions
نویسندگان
چکیده
We construct nonlinear entire solutions in $\mathbb{R}^6$ to equations of minimal surface type that correspond parametric elliptic functionals.
منابع مشابه
Entire Invariant Solutions to Monge-ampère Equations
We prove existence and regularity of entire solutions to MongeAmpère equations invariant under an irreducible action of a compact Lie group. We consider Monge-Ampère equations of the form f(∇φ) detDijφ = g(x) (0.1) where f and g are nonnegative measurable functions on R. We recall first the concept of a weak solution of (0.1). Let φ be a convex function. Then ∇φ is a well-defined multi-valued m...
متن کاملEntire Large Solutions of Quasilinear Elliptic Equations of Mixed Type
In this paper, the existence and nonexistence of nonnegative entire large solutions for the quasilinear elliptic equation 2 | | = ( ) ( ) ( ) ( ) m div u u p x f u q x g u are established, where 2 m , f and g are nondecreasing and vanish at the origin. The locally H older continuous functions p and q are nonnegative. We extend results previously obtained for special cases of f a...
متن کاملENTIRE SOLUTIONS OF FERMAT TYPE q-DIFFERENCE DIFFERENTIAL EQUATIONS
In this article, we describe the finite-order transcendental entire solutions of Fermat type q-difference and q-difference differential equations. In addition, we investigate the similarities and other properties among those solutions.
متن کاملA Hölder Estimate for Entire Solutions to the Two-valued Minimal Surface Equation
We prove a Hölder estimate near infinity for solutions to the twovalued minimal surface equation over R2 \ {0}, and give a Bernstein-type theorem in case the solution can be extended continuously across the origin. The main results follow by modifying methods used to study exterior solutions to equations of minimal surface type.
متن کاملEntire solutions of nonlinear differential-difference equations
In this paper, we describe the properties of entire solutions of a nonlinear differential-difference equation and a Fermat type equation, and improve several previous theorems greatly. In addition, we also deduce a uniqueness result for an entire function f(z) that shares a set with its shift [Formula: see text], which is a generalization of a result of Liu.
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: Journal of the European Mathematical Society
سال: 2021
ISSN: ['1435-9855', '1435-9863']
DOI: https://doi.org/10.4171/jems/1202