p(x)-Harmonic functions with unbounded exponent in a subdomain

speaker: José Miguel Urbano (CMUC - University of Coimbra, Portugal)

abstract: We study the Dirichlet problem for the p(x)-Laplacian, in the case of a variable exponent p(x) that is infinite in a subdomain D. The main issue is to give a proper sense to what a solution is. To this end, we consider the limit of the solutions u_n to the corresponding problem when p_n(x) = min (p(x),n), in particular, with p_n=n in D. Under suitable assumptions on the data, we find that such a limit exists and that it can be characterized as the unique solution of a variational minimization problem, which is, in addition, infinity-harmonic within D. Moreover, we examine this limit in the viscosity sense and find the boundary value problem it solves.

This is a joint work with Juan J. Manfredi and Julio D. Rossi.

timetable:
Thu 17 Sep, 16:30 - 17:30, Aula Dini
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