Anisotropic 1-Laplacian problems with unbounded weights
2021 ◽
Vol 28
(6)
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Keyword(s):
AbstractIn this work we prove the existence of nontrivial bounded variation solutions to quasilinear elliptic problems involving a weighted 1-Laplacian operator. A key feature of these problems is that weights are unbounded. One of our main tools is the well-known Caffarelli-Kohn-Nirenberg’s inequality, which is established in the framework of weighted spaces of functions of bounded variation (and that provides us the necessary embeddings between weighted spaces). Additional tools are suitable variants of the Mountain Pass Theorem as well as an extension of the pairing theory by Anzellotti to this new setting.
2000 ◽
Vol 02
(01)
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pp. 47-59
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1991 ◽
Vol 43
(3)
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pp. 449-460
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2014 ◽
Vol 54
(3)
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pp. 474-490
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2013 ◽
Vol 58
(6)
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pp. 795-811
2003 ◽
Vol 131
(8)
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pp. 2409-2414
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