In this paper, we prove some regularity results for a noncoercive nonlinear Dirichlet problem in an unbounded domain. The main result is obtained in the hypothesis that suitable coefficients of the operator associated to the problem belong to a class of functional spaces strictly containing Lebesgue ones. This can be done by approximation via coercive nonlinear Dirichlet problems. Under additional assumptions, we also get the boundedness of a solution.
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Emilia Anna Alfano, Patrizia Di Gironimo, Sara Monsurrò, Regularity results for a noncoercive nonlinear Dirichlet problem. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 33 (2022), no. 1, pp. 139–159DOI 10.4171/RLM/967