The purpose of this paper is to investigate the Cahn-Hillard approximation for entire minimal hypersurfaces in the hyperbolic space. Combining comparison principles with minimization and blow-up arguments, we prove existence results for entire local minimizers with prescribed behavior at infinity. Then, we study the limit as the length scale tends to zero through a Γ-convergence analysis, obtaining existence of entire minimal hypersurfaces with prescribed boundary at infinity. In particular, we recover some existence results proved in [3, 21] using geometric measure theory. © Taylor & Francis Group, LLC.

Phase transitions and minimal hypersurfaces in hyperbolic space / Pisante, Adriano; Ponsiglione, Marcello. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 36:5(2011), pp. 819-849. [10.1080/03605302.2010.531339]

Phase transitions and minimal hypersurfaces in hyperbolic space

PISANTE, Adriano;PONSIGLIONE, Marcello
2011

Abstract

The purpose of this paper is to investigate the Cahn-Hillard approximation for entire minimal hypersurfaces in the hyperbolic space. Combining comparison principles with minimization and blow-up arguments, we prove existence results for entire local minimizers with prescribed behavior at infinity. Then, we study the limit as the length scale tends to zero through a Γ-convergence analysis, obtaining existence of entire minimal hypersurfaces with prescribed boundary at infinity. In particular, we recover some existence results proved in [3, 21] using geometric measure theory. © Taylor & Francis Group, LLC.
2011
variational methods; boundary value problems; minimal hypersurfaces; hyperbolic space; phase transitions
01 Pubblicazione su rivista::01a Articolo in rivista
Phase transitions and minimal hypersurfaces in hyperbolic space / Pisante, Adriano; Ponsiglione, Marcello. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 36:5(2011), pp. 819-849. [10.1080/03605302.2010.531339]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/379993
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