Advances in Differential Equations

Existence of ground states and free-boundary problems for the prescribed mean-curvature equation

Monica Conti and Filippo Gazzola

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Abstract

Existence and nonexistence of radially symmetric ground states and compact support solutions for a quasilinear equation involving the mean-curvature operator are studied in dependence of the parameters involved. Different tools are used in the proofs, according to the cases considered. Several numerical results are also given: the experiments show a possible lack of uniqueness of the solution and a strong dependence on the space dimension.

Article information

Source
Adv. Differential Equations Volume 7, Number 6 (2002), 667-694.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651733

Mathematical Reviews number (MathSciNet)
MR1894862

Zentralblatt MATH identifier
1208.35181

Subjects
Primary: 35R35: Free boundary problems
Secondary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 35J60: Nonlinear elliptic equations 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

Citation

Conti, Monica; Gazzola, Filippo. Existence of ground states and free-boundary problems for the prescribed mean-curvature equation. Adv. Differential Equations 7 (2002), no. 6, 667--694. https://projecteuclid.org/euclid.ade/1356651733.


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