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{\bf Jan Mal\'y}\\
Charles University\\
 Prague, Czech Republic\\
{\tt maly@karlin.mff.cuni.cz}
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\centerline{\it Weak Forms of Jacobian and Hessian}

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\noindent {\bf Abstract}:  This talk is presentation of a joint work with Irene Fonseca. We study weak continuity properties of the Hessian and
relaxation of the functional
$$
F_H(u,\Omega)=\int_{\Omega} |\det\nabla ^2u|\,dx
$$
in connection with pointwise Hessian and weak forms
of the Hessian.

Also, we revisit the theory of weak Jacobian, mostly for comparison,
but some results obtained at this occasion seem to be new.

In particular, one cannot expect in general that mollifications of the
weak Jacobian or Hessian converge a.e. to the pointwise Jacobian or Hessian.
The situation is better if the weak Jacobian (Hessian) is a measure.
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