The prescribed mean curvature equation in weakly regular domains

The prescribed mean curvature equation in weakly regular domains We show that the characterization of existence and uniqueness up to vertical translations of solutions to the prescribed mean curvature equation, originally proved by Giusti in the smooth case, holds true for domains satisfying very mild regularity assumptions. Our results apply in particular to the non-parametric solutions of the capillary problem for perfectly wetting fluids in zero gravity. Among the essential tools used in the proofs, we mention a generalized Gauss–Green theorem based on the construction of the weak normal trace of a vector field with bounded divergence, in the spirit of classical results due to Anzellotti, and a weak Young’s law for $$(\Lambda ,r_{0})$$ ( Λ , r 0 ) -minimizers of the perimeter. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Differential Equations and Applications NoDEA Springer Journals

The prescribed mean curvature equation in weakly regular domains

Loading next page...
 
/lp/springer_journal/the-prescribed-mean-curvature-equation-in-weakly-regular-domains-S0VuCj80L4
Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis
ISSN
1021-9722
eISSN
1420-9004
D.O.I.
10.1007/s00030-018-0500-3
Publisher site
See Article on Publisher Site

Abstract

We show that the characterization of existence and uniqueness up to vertical translations of solutions to the prescribed mean curvature equation, originally proved by Giusti in the smooth case, holds true for domains satisfying very mild regularity assumptions. Our results apply in particular to the non-parametric solutions of the capillary problem for perfectly wetting fluids in zero gravity. Among the essential tools used in the proofs, we mention a generalized Gauss–Green theorem based on the construction of the weak normal trace of a vector field with bounded divergence, in the spirit of classical results due to Anzellotti, and a weak Young’s law for $$(\Lambda ,r_{0})$$ ( Λ , r 0 ) -minimizers of the perimeter.

Journal

Nonlinear Differential Equations and Applications NoDEASpringer Journals

Published: Feb 23, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off