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Singular Anisotropic Double Phase Problems

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Abstract

We consider three kinds of anisotropic double phase problems with Dirichlet boundary condition. In two of them we have strong singularity and an unbounded coefficient. Using variational method together with truncation, comparison and approximation techniques, we prove existence and multiplicity theorems for our problem.

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Acknowledgements

The authors wish to thank a very knowledgeable referee for her/his valuable corrections and remarks.

Funding

This work has been supported by Piano della Ricerca di Ateneo 2020-2022– PIACERI: Project MO.S.A.I.C. “Monitoraggio satellitare, modellazioni matematiche e soluzioni architettoniche e urbane per lo studio, la previsione e la mitigazione delle isole di calore urbano”, Project EEEP &DLaD. S. Leonardi is member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilit’a e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM), codice CUP E55F22000270001.

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Author notes

  1. S. Leonardi, N.S. Papageorgiou have contributed equally to this work.

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria, 6, 95125, Catania, Italy

    Salvatore Leonardi

  2. Department of Mathematics, Technical University, Zorografou Campus, 15780, Athens, Greece

    Nikolaos S. Papageorgiou

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  1. Salvatore Leonardi
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  2. Nikolaos S. Papageorgiou
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Correspondence to Salvatore Leonardi.

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Leonardi, S., Papageorgiou, N.S. Singular Anisotropic Double Phase Problems. Results Math 78, 73 (2023). https://doi.org/10.1007/s00025-023-01860-3

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