Blow-up analysis for the prescribed mean curvature equation on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mi mathvariant="double-struck">R</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>

Caldiroli, Paolo

doi:10.1016/j.jfa.2008.12.003

Journal of Functional Analysis

2009

DOI: 10.1016/j.jfa.2008.12.003

|View full text |Cite

Blow-up analysis for the prescribed mean curvature equation onR2

Paolo Caldiroli

Abstract: We consider theWe show that a sequence of approximate solutions of the H -system on R 2 admits a limit configuration made byH -bubbles, namely nonconstant solutions ofH -systems on R 2 , andH can be the mapping H or the constant H ∞ .

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2011

2018

Publication Types

Select...

Article3

Relationship

Self Cite1

Independent2

Authors

Journals

Cited by 3 publications

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Isovolumetric and Isoperimetric Problems for a Class of Capillarity Functionals

Caldiroli

2015

Arch Rational Mech Anal

Self Cite

View full text Add to dashboard Cite

Capillarity functionals are parameter invariant functionals defined on classes of two-dimensional parametric surfaces in R 3 as the sum of the area integral and an anisotropic term of suitable form. In the class of parametric surfaces with the topological type of S 2 and with fixed volume, extremals of capillarity functionals are surfaces whose mean curvature is prescribed up to a constant. For a certain class of anisotropies vanishing at infinity, we prove existence and nonexistence of volumeconstrained, S 2 -type, minimal surfaces for the corresponding capillarity functionals. Moreover, in some cases, we show existence of extremals for the full isoperimetric inequality.

show abstract

Isovolumetric and Isoperimetric Problems for a Class of Capillarity Functionals

Caldiroli

2015

Arch Rational Mech Anal

Self Cite

View full text Add to dashboard Cite

show abstract

Bubbles with prescribed mean curvature: The variational approach

Caldiroli

Musina

2011

Nonlinear Analysis: Theory, Methods & Applications

View full text Add to dashboard Cite

Existence of isovolumetric $\mathbb S^2$-type stationary surfaces for capillarity functionals

Caldiroli

Iacopetti

2018

Rev. Mat. Iberoam.

View full text Add to dashboard Cite

Capillarity functionals are parameter invariant functionals defined on classes of two-dimensional parametric surfaces in R 3 as the sum of the area integral and a non homogeneous term of suitable form. Here we consider the case of a class of non homogenous terms vanishing at infinity for which the corresponding capillarity functional has no volume-constrained S 2 -type minimal surface. Using variational techniques, we prove existence of extremals characterized as saddle-type critical points.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Blow-up analysis for the prescribed mean curvature equation onR2

Abstract: We consider theWe show that a sequence of approximate solutions of the H -system on R 2 admits a limit configuration made byH -bubbles, namely nonconstant solutions ofH -systems on R 2 , andH can be the mapping H or the constant H ∞ .

Cited by 3 publications

References 17 publications

Isovolumetric and Isoperimetric Problems for a Class of Capillarity Functionals

Isovolumetric and Isoperimetric Problems for a Class of Capillarity Functionals

Bubbles with prescribed mean curvature: The variational approach

Existence of isovolumetric $\mathbb S^2$-type stationary surfaces for capillarity functionals

Contact Info

Product

Resources

About