Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints
Second-Order Boundary regularity for quasilinear variational inequalities.
Semiconcavity results for optimal control problems admitting no singular minimizing controls
Semipermeable surfaces for non-smooth differential inclusions
We investigate the regularity of semipermeable surfaces along barrier solutions without the assumption of smoothness of the right-hand side of the differential inclusion. We check what can be said if the assumptions concern not the right-hand side itself but the cones it generates. We examine also the properties of families of sets with semipermeable boundaries.
Sharp summability for Monge transport density via interpolation
Using some results proved in De Pascale and Pratelli [Calc. Var. Partial Differ. Equ. 14 (2002) 249-274] (and De Pascale et al. [Bull. London Math. Soc. 36 (2004) 383-395]) and a suitable interpolation technique, we show that the transport density relative to an source is also an function for any .
Sharp summability for Monge Transport density via Interpolation
Using some results proved in De Pascale and Pratelli [Calc. Var. Partial Differ. Equ.14 (2002) 249-274] (and De Pascale et al. [Bull. London Math. Soc.36 (2004) 383-395]) and a suitable interpolation technique, we show that the transport density relative to an Lp source is also an Lp function for any .
Singular minimisers in the calculus of variations : a degenerate form of cavitation
Smoothness properties of solutions to the nonlinear Stokes problem with nonautonomous potentials
We discuss regularity results concerning local minimizers of variational integrals like defined on energy classes of solenoidal fields. For the potential we assume a -elliptic growth condition. In the situation without -dependence it is known that minimizers are of class on an open subset of with full measure if (for we have ). In this article we extend this to the case of nonautonomous integrands. Of course our result extends to weak solutions of the corresponding nonlinear...
Some concepts of regularity for parametric multiple-integral problems in the calculus of variations
We show that asserting the regularity (in the sense of Rund) of a first-order parametric multiple-integral variational problem is equivalent to asserting that the differential of the projection of its Hilbert-Carathéodory form is multisymplectic, and is also equivalent to asserting that Dedecker extremals of the latter -form are holonomic.
Some regularity results for minimal crystals
We introduce an intrinsic notion of perimeter for subsets of a general Minkowski space ( a finite dimensional Banach space in which the norm is not required to be even). We prove that this notion of perimeter is equivalent to the usual definition of surface energy for crystals and we study the regularity properties of the minimizers and the quasi-minimizers of perimeter. In the two-dimensional case we obtain optimal regularity results: apart from a singular set (which is -negligible and is empty...
Some regularity results for minimal crystals
We introduce an intrinsic notion of perimeter for subsets of a general Minkowski space (i.e. a finite dimensional Banach space in which the norm is not required to be even). We prove that this notion of perimeter is equivalent to the usual definition of surface energy for crystals and we study the regularity properties of the minimizers and the quasi-minimizers of perimeter. In the two-dimensional case we obtain optimal regularity results: apart from a singular set (which is -negligible and is...
Some remarks on the regularity of minimizers of integrals with anisotropic growth
We prove higher integrability for minimizers of some integrals of the calculus of variations; such an improved integrability allows us to get existence of weak second derivatives.
Some remarks on uniqueness and regularity of Cheeger sets
Some remarks on variational problems for functionals with growth
Stability and sensitivity analysis for optimal control problems with a first-order state constraint and application to continuation methods
The paper deals with an optimal control problem with a scalar first-order state constraint and a scalar control. In presence of (nonessential) touch points, the arc structure of the trajectory is not stable. Under some reasonable assumptions, we show that boundary arcs are structurally stable, and that touch point can either remain so, vanish or be transformed into a single boundary arc. Assuming a weak second-order optimality condition (equivalent to uniform quadratic growth), stability and...
Stable approximations of a minimal surface problem with variational inequalities.
Structure of entropy solutions to the eikonal equation
Structure of stable solutions of a one-dimensional variational problem
We prove the periodicity of all H2-local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear double...
Summability of the solutions of nonlinear elliptic equations with right hand side measures.
Symmetry and monotonicity of solutions to some variational problems in cylinders and annuli.