  The effective piezoelectric coefficients of twin walls in tetragonal
ferroelectric are calculated in the framework of decoupling approximation and
Landau-Ginzburg-Devonshire theory allowing for polarization gradient terms,
electrostriction and flexoelectric coupling. Using an example of piezoelectric
response of a1-a2 twins to a homogeneous electric field, we show that the
response is almost independent on the flexoelectric coupling, but is very
sensitive to the values of polarization gradient coefficients. This behavior
originates from the strong coupling between local dielectric susceptibility and
the gradient coefficients. The enhancement of piezoelectric response from 10%
up to a factor of 103 times is predicted. The local electromechanical response
of the domain walls can thus provide information on the gradient terms in GLD
expansion and pinning mechanisms of the ferroelectric domain walls. The
observability of these effects by the piezoresponse force microscopy of
electroded structures and impact on the functional properties of the systems
with dense domain structures is analyzed
