Advances in Differential Equations

On Palais-Smale sequences for $H$-systems: some examples

Paolo Caldiroli and Roberta Musina

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We exhibit a series of examples of Palais-Smale sequences for the Dirichlet problem associated to the mean curvature equation with null boundary condition, and we show that in the case of nonconstant mean curvature functions different kinds of blow up phenomena appear and Palais-Smale sequences may have quite wild behaviour.

Article information

Adv. Differential Equations, Volume 11, Number 8 (2006), 931-960.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J20: Variational methods for second-order elliptic equations 49J10: Free problems in two or more independent variables 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)


Caldiroli, Paolo; Musina, Roberta. On Palais-Smale sequences for $H$-systems: some examples. Adv. Differential Equations 11 (2006), no. 8, 931--960.

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