## Illinois Journal of Mathematics

### The Dirichlet problem for the constant mean curvature equation in $\operatorname{Sol}_{3}$

#### Abstract

We prove a version of the Jenkins–Serrin theorem for the existence of constant mean curvature graphs over bounded domains with infinite boundary data in $\operatorname{Sol}_{3}$. Moreover, we construct examples of admissible domains where the results may be applied.

#### Article information

Source
Illinois J. Math., Volume 63, Number 2 (2019), 259-297.

Dates
Revised: 12 April 2019
First available in Project Euclid: 1 August 2019

https://projecteuclid.org/euclid.ijm/1564646433

Digital Object Identifier
doi:10.1215/00192082-7768727

Mathematical Reviews number (MathSciNet)
MR3987497

Zentralblatt MATH identifier
07088307

#### Citation

Klaser, Patricía; Menezes, Ana. The Dirichlet problem for the constant mean curvature equation in $\operatorname{Sol}_{3}$. Illinois J. Math. 63 (2019), no. 2, 259--297. doi:10.1215/00192082-7768727. https://projecteuclid.org/euclid.ijm/1564646433

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