Hölder continuity for continuous solutions of the singular minimal surface equation with arbitrary zero set

2017 ◽  
Vol 56 (1) ◽  
Author(s):  
Tobias Tennstädt
Keyword(s):  
Minimal Surface ◽  
Hölder Continuity ◽  
Zero Set ◽  
Holder Continuity ◽  
Continuous Solutions ◽  
Surface Equation ◽  
Minimal Surface Equation ◽  
Singular Minimal Surface

scholarly journals Symmetric solutions of the singular minimal surface equation

2021 ◽  
Author(s):  
Ulrich Dierkes ◽  
Nico Groh
Keyword(s):  
Minimal Surface ◽  
Bernstein Type ◽  
Surface Equation ◽  
Minimal Surface Equation ◽  
Singular Minimal Surface

AbstractWe classify all rotational symmetric solutions of the singular minimal surface equation in both cases $$\alpha <0$$ α < 0 and $$\alpha >0$$ α > 0 . In addition, we discuss further geometric and analytic properties of the solutions, in particular stability, minimizing properties and Bernstein-type results.

Existence and Hölder continuity to solutions of the complex Monge–Ampère-type equations with measures vanishing on pluripolar subsets

2021 ◽  
Author(s):  
Le Mau Hai ◽  
Vu Van Quan
Keyword(s):  
Pseudoconvex Domain ◽  
Hölder Continuity ◽  
Type Equation ◽  
Holder Continuity ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Strictly Pseudoconvex Domain ◽  
Monge Ampere

In this paper, we establish existence of Hölder continuous solutions to the complex Monge–Ampère-type equation with measures vanishing on pluripolar subsets of a bounded strictly pseudoconvex domain [Formula: see text] in [Formula: see text].

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