We study the existence and regularity of minimizers of an energy functional which in the physical 3D dimension corresponds to the so–called generalized Varga materials and includes an additional term accounting for surface tension. Due to the linear growth of the strain energy, we relax the problem in a suitable class of extended graphs of radially symmetric functions of bounded variations. Besides cavitation at the origin, a new phenomenon due to the occurrence of a spherical fracture inside the body is observed.
On Generalized Varga Materials / Celada, P., Mucci, D.. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - 209:3(2026), pp. 1-43. [10.1007/s10957-026-03018-x]
On Generalized Varga Materials
Celada, Pietro;Mucci, Domenico
2026
Abstract
We study the existence and regularity of minimizers of an energy functional which in the physical 3D dimension corresponds to the so–called generalized Varga materials and includes an additional term accounting for surface tension. Due to the linear growth of the strain energy, we relax the problem in a suitable class of extended graphs of radially symmetric functions of bounded variations. Besides cavitation at the origin, a new phenomenon due to the occurrence of a spherical fracture inside the body is observed.
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