CRM: Centro De Giorgi
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Dispersive and subelliptic PDEs

Average solutions to linear second order semielliptic PDEs

speaker: Ermanno Lanconelli (Università di Bologna)

abstract: Let L be a linear second order PDO with nonegatve characteristic form (semielliptic, in short). Assume L hypoelliptic, in divergence form and endowed with a well-behaved fundamental solution G. Then, solutions and subsolutions to Lu= 0 can be characterized in terms of suitable average operators on the level sets of G. These average operators can be also used : 1) to define ''asymptotic-average'' solutions and subsolutions, and to extend to the operator L classical results by Pizzetti, Blaschke, Privaloff, Rado' and Beckenbach. 2) to solve the Dirichlet problem for the Poisson-type equation Lu = f, for every continuous function f.

Tue 11 Feb, 14:00 - 14:50, Aula Dini


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