Elliptic equations in dimension 2 with double exponential nonlinearities

By Marta Calanchi, Bernhard Ruf, Federica Sani. 2017

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A boundary value problem on the unit disk in $$\mathbb R^2$$R2 is considered, involving an elliptic operator with a singular weight of logarithmic type and nonlinearities which are subcritical or critical with respect to the associated gradient norm. The existence of non-trivial solutions is proved, relying on variational methods. In the critical case, the associated energy functional is non-compact. A suitable asymptotic condition allows to avoid the non-compactness levels of the functional.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/80a0a1180d1ff9a0e48012ce223bd48a3b5c665c