Elliptic 1-Laplacian equations with dynamical boundary conditions

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2018

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This paper is concerned with an evolution problem having an elliptic equation involving the 1-Laplacian operator and a dynamical boundary condition. We apply nonlinear semigroup theory to obtain existence and uniqueness results as well as a comparison principle. Our main theorem shows that the solution we found is actually a strong solution. We also compare solutions with different data.

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Marta Latorre, Sergio Segura de León, Elliptic 1-Laplacian equations with dynamical boundary conditions, Journal of Mathematical Analysis and Applications, Volume 464, Issue 2, 2018, Pages 1051-1081, ISSN 0022-247X, https://doi.org/10.1016/j.jmaa.2018.02.006.
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