Regularity of Free Boundaries in Anisotropic Capillarity Problems and the Validity of Young’s Law
نویسنده
چکیده
Local volume-constrained minimizers in anisotropic capillarity problems develop free boundaries on the walls of their containers. We prove the regularity of the free boundary outside a closed negligible set, showing in particular the validity of Young’s law at almost every point of the free boundary. Our regularity results are not specific to capillarity problems, and actually apply to sets of finite perimeter (and thus to codimension one integer rectifiable currents) arising as minimizers in other variational problems with free boundaries.
منابع مشابه
Dimensional Estimates for Singular Sets in Geometric Variational Problems with Free Boundaries
We show that singular sets of free boundaries arising in codimension one anisotropic geometric variational problems are Hn−3-negligible, where n is the ambient space dimension. In particular our results apply to capillarity type problems, and establish everywhere regularity in the three-dimensional case.
متن کاملAsymptotic Expansions of the Contact Angle in Nonlocal Capillarity Problems
We consider a family of nonlocal capillarity models, where surface tension is modeled by exploiting the family of fractional interaction kernels |z|−n−s, with s ∈ (0, 1) and n the dimension of the ambient space. The fractional Young’s law (contact angle condition) predicted by these models coincides, in the limit as s → 1−, with the classical Young’s law determined by the Gauss free energy. Her...
متن کاملExact Radial Free Vibration Frequencies of Power-Law Graded Spheres
This study concentrates on the free pure radial vibrations of hollow spheres made of hypothetically functionally simple power rule graded materials having identical inhomogeneity indexes for both Young’s modulus and the density in an analytical manner. After offering the exact elements of the free vibration coefficient matrices for free-free, free-fixed, and fixed-fixed restraints, a parametric...
متن کاملThe regularity of history and its features in the Qur’an
The regularity of history, the nature of the law of history, the method of how dealing with the regularity of history under related verses of the Qur’an, and the category of the factor of the law of history, all fall in the domain of theoretical philosophizing about history in the light of Qur’anic approach. From among the features of the law of history in the light of the Qur’an mention can be...
متن کاملDynamic Behavior of Anisotropic Protein Microtubules Immersed in Cytosol Via Cooper–Naghdi Thick Shell Theory
In the present research, vibrational behavior of anisotropic protein microtubules (MTs) immersed in cytosol via Cooper–Naghdi shell model is investigated. MTs are hollow cylindrical structures in the eukaryotic cytoskeleton which surrounded by filament network. The temperature effect on vibration frequency is also taken into account by assuming temperature-dependent material properties for MTs....
متن کامل