Dirichlet problems involving the 1-Laplacian

The present paper concerns Dirichlet problem for a class of non-linear partial differential equations involving 1-Laplacian. The non-linear term holds the sub-critical exponential growth and guarantees the solution is non-trivial. The difficulty provided by the degeneration of 1-Laplacian has been o...

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Bibliographic Details
Published in:	Journal of pseudo-differential operators and applications Vol. 11; no. 4; pp. 1897 - 1913
Main Authors:	Wei, Yawei, Zhao, Huiying
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01-12-2020 Springer Nature B.V
Subjects:	Algebra Analysis Applications of Mathematics Degeneration Dirichlet problem Fields (mathematics) Functional Analysis Mathematics Mathematics and Statistics Nonlinear differential equations Nonlinear equations Operator Theory Partial Differential Equations Non-linear equations 35J60 Dirichlet problems 35J70 35A01 Non-smooth analysis 1-Laplacian
Online Access:	Get full text
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Summary:	The present paper concerns Dirichlet problem for a class of non-linear partial differential equations involving 1-Laplacian. The non-linear term holds the sub-critical exponential growth and guarantees the solution is non-trivial. The difficulty provided by the degeneration of 1-Laplacian has been overcame by a replacement with a suitable vector field. The underlying minimization problem has been investigated to verify the existence result to the concern problem.
ISSN:	1662-9981 1662-999X
DOI:	10.1007/s11868-020-00342-2