Seminario di analisi matematica
ore
14:00
presso Seminario II
The maximal regularity in L^p (1<p<∞) for the solution of a linear abstract Cauchy
problem (1) u'(t) + Lu(t) = f(t), (2) u(0) = 0 where the unknown function u and the
given function f are defined on [0,T] with values in a Banach space X, is the requirement
that for any f∈L^p(0,T ; X) the Cauchy problem (1) - (2) has a unique solution and
that u' and Au belong to L^p(0,T; X) and depend continuously on f in L^p(0,T; X). This
problem can be stated in a more abstract form as the problem of solving the equation
Au + Bu = f in the space Y = L^p(0,T; X) for appropriate operators A and B acting in
Y. In these two seminars I will speak of a result that gives conditions on A, B and X to
ensure the bounded invertibility of the operator A+B, and hence the maximal regularity
for the solutions of the Cauchy problem.