Some New Insights on the Maximum Principle

Prof. Antonio Tarsia, Università di Pisa

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Abstract. By establishing De Giorgi type level estimates for functions in W 1,t(Ω), Ω ⊂ RN , with t > N ≥2, we prove a new Harnack type inequality for functions which do not necessarily belong to De Giorgi’s classes, as obtained by Benedetto-Trudinger for function W 1,p(Ω), p > 1

As a consequence, we prove the validity of the strong maximum principle for a class of uniformly elliptic operators of order greater than two in fairly general domains. (Joint work with D. Cassani).

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