Wellposedness and the Lavrentiev Phenomenon
T. Zolezzi · SIAM Journal on Control and Optimization · 1992
The Lavrentiev phenomenon in the calculus of variations is viewed and handled as a value Hadamard illposedness problem. Regularization is obtained by a decoupling technique of Ball–Knowles via a variational convergence approach. In this way we extend known one-dimensional results, simplifying their proofs. The same approach yields regularization for problems involving multiple integrals. A criterion for Hadamard wellposedness of multiple integrals is presented, and a new sufficient condition for nonoccurrence of the one-dimensional phenomenon is obtained.