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Giaquinta is well known for his basic work in elliptic regularity theory, and especially in the setting of vectorial variational problems. Together with Enrico Giusti he has obtained innovative results[4][5][6] on the regularity of minima of variational integrals and related singular sets. The main novelty is in the fact that, for the first time, the regularity of minimizers is obtained using directly the minimality properties without appealing to Euler–Lagrange equation of the functionals, which in general is not supposed to exist in the cases considered. His work with Giuseppe Modica on the local higher integrability properties of solutions to elliptic systems has had an influence on the development of partial regularity theory. Many of these results are summarized in his 1983 book.
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Lettera Matematica Pristemno. 1 (2017): 116-121
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