Some remarks on the regularity of minimizers

1988 ◽  
pp. 95-103
Author(s):  
Mariano Giaquinta
Keyword(s):  
Regularity Of Minimizers

Regularity of minimizers under limit growth conditions

2017 ◽  
Vol 153 ◽  
pp. 294-310 ◽  
Author(s):  
Giovanni Cupini ◽  
Paolo Marcellini ◽  
Elvira Mascolo
Keyword(s):  
Growth Conditions ◽  
Regularity Of Minimizers

scholarly journals Analytical validation of the Young–Dupré law for epitaxially-strained thin films

2019 ◽  
Vol 29 (12) ◽  
pp. 2183-2223 ◽  
Author(s):  
Elisa Davoli ◽  
Paolo Piovano
Keyword(s):  
Thin Films ◽  
Contact Point ◽  
Variational Model ◽  
Analytical Validation ◽  
Regularity Of Minimizers ◽  
Transmission Problems ◽  
Thin Film Model ◽  
New Ideas ◽  
Film Substrate ◽  
Regularity Results

We present here an analysis of the regularity of minimizers of a variational model for epitaxially strained thin-films. The regularity of energetically-optimal film profiles is studied by extending previous methods and by developing new ideas based on transmission problems. The achieved regularity results relate to both the Stranski-Krastanow and the Volmer-Weber modes, the possibility of different elastic properties between the film and the substrate, and the presence of the surface tensions of all three involved interfaces: film/gas, substrate/gas, and film/substrate. Finally, geometrical conditions are provided for the optimal wetting angle, i.e. the angle formed at the contact point of films with the substrate. In particular, the Young–Dupré law is shown to hold, yielding what appears to be the first analytical validation of such law for a thin-film model in the context of Continuum Mechanics.

Traceless Maps as the Singular Minimizers in the Multi-dimensional Calculus of Variations

2017 ◽  
Vol 60 (3) ◽  
pp. 631-640
Author(s):  
M. S. Shahrokhi-Dehkordi
Keyword(s):  
Convex Function ◽  
Energy Functional ◽  
Uniformly Convex ◽  
Lagrange Equations ◽  
Regularity Of Minimizers ◽  
Uniformly Convex Function ◽  
Bounded Lipschitz Domain ◽  
Second Derivatives ◽  
Image Position ◽  
Singular Minimizers

AbstractLet Ω ⊂ ℝn be a bounded Lipschitz domain and consider the energy functionalover the space of W1,2(Ω, ℝm) where the integrand is a smooth uniformly convex function with bounded second derivatives. In this paper we address the question of regularity for solutions of the corresponding system of Euler–Lagrange equations. In particular, we introduce a class of singularmaps referred to as traceless and examine themas a new counterexample to the regularity of minimizers of the energy functional ℱ[ ·, Ω] using a method based on null Lagrangians.

scholarly journals Regularity of minimizers of shape optimization problems involving perimeter

2018 ◽  
Vol 109 ◽  
pp. 147-181 ◽  
Author(s):  
Guido De Philippis ◽  
Jimmy Lamboley ◽  
Michel Pierre ◽  
Bozhidar Velichkov
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Regularity Of Minimizers

Regularity of minimizers for higher order variational problems in one independent variable

2011 ◽  
Vol 35 (2) ◽  
pp. 172-177 ◽  
Author(s):  
Christos Gavriel ◽  
Sofia Lopes ◽  
Richard Vinter
Keyword(s):  
Variational Problems ◽  
Higher Order ◽  
Regularity Of Minimizers ◽  
Independent Variable
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