A direct proof of the Tonelli's partial regularity result
A Ferriero - Discrete and Continuous Dynamical Systems, 2012 - aimsciences.org
The aim of this work is to give a simple proof of the Tonelli's partial regularity result which
states that any absolutely continuous solution to the variational problem $$\min\left\{\int_a^ b …
states that any absolutely continuous solution to the variational problem $$\min\left\{\int_a^ b …
Singular sets and the Lavrentiev phenomenon
R Gratwick - Proceedings of the Royal Society of Edinburgh Section …, 2015 - cambridge.org
We show that non-occurrence of the Lavrentiev phenomenon does not imply that the
singular set is small. Precisely, given a compact Lebesgue null subset E⊆ ℝ and an …
singular set is small. Precisely, given a compact Lebesgue null subset E⊆ ℝ and an …
Relaxation and regularity in the calculus of variations
A Ferriero - Journal of Differential Equations, 2010 - Elsevier
In this work we prove that, if L (t, u, ξ) is a continuous function in t and u, Borel measurable in
ξ, with bounded non-convex pieces in ξ, then any absolutely continuous solution u¯ to the …
ξ, with bounded non-convex pieces in ξ, then any absolutely continuous solution u¯ to the …
Variations, approximation, and low regularity in one dimension
R Gratwick - Calculus of Variations and Partial Differential …, 2017 - Springer
We investigate the properties of minimizers of one-dimensional variational problems when
the Lagrangian has no higher smoothness than continuity. An elementary approximation …
the Lagrangian has no higher smoothness than continuity. An elementary approximation …