Approximation of Quasiconvex Functions, and Lower Semicontinuity of Multiple Integrals.
On the definition and the lower semicontinuity of certain quasiconvex integrals
Everywhere regularity for a class of elliptic systems without growth conditions
A general approach to the existence of minimizers of one-dimensional non-coercive integrals of the calculus of variations
Implicit second order partial differential equations
Relaxation of non convex variational problems
Si danno condizioni necessarie affinché un integrale del calcolo delle variazioni risulti sequenzialmente semicontinuo inferiormente nella topologia debole di e si prova che il massimo funzionale semicontinuo inferiormente minorante è ancora un integrale del calcolo delle variazioni. Ne consegue un teorema di «rilassamento» nel senso di Ekeland e Temam [1].
An existence result for a nonconvex variational problem via regularity
Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The -dependence, explicitly appearing in the integrands, adds significant technical difficulties in the proof.
An explicit solution to a system of implicit differential equations
Topological degree, Jacobian determinants and relaxation
A characterization of the total variation of the Jacobian determinant is obtained for some classes of functions outside the traditional regularity space . In particular, explicit formulas are deduced for functions that are locally Lipschitz continuous away from a given one point singularity . Relations between and the distributional determinant are established, and an integral representation is obtained for the relaxed energy of certain polyconvex functionals at maps .
An existence result for a nonconvex variational problem via regularity
Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are . In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands with respect to the gradient variable. The -dependence, explicitly appearing in the integrands, adds significant technical difficulties in the proof.
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