| We establish sufficient conditions for Lipschitz extremals of integral functionals to be strong local minimizers. We also prove a regularity theorem for those extremals that satisfy our sufficient conditions. Our sufficiency theorem has to be compared with the Grabovsky and Mengesha sufficiency result for smooth extremals, in view of the observation by Kristensen and Taheri that their sufficient conditions do not apply to merely Lipschitz extremals. In this thesis we replace the uniform quasiconvexity condition with a new, much stronger condition that works for non-smooth Lipschitz extremals. We also show that those extremals that satisfy our new condition must be more regular than merely Lipschitz. |
