Differential and Integral Equations

The $1$--Laplacian elliptic equation with inhomogeneous Robin boundary conditions

José M. Mazón, Julio D. Rossi, and Sergio Segura de León

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In this paper, we study existence of solutions to the $1$--Laplacian elliptic equation with inhomogeneous Robin boundary conditions. It is also analyzed from the point of view of the Euler--Lagrange equation of a lower semicontinuous functional. We see the equivalence between the solutions of the elliptic problem and the minimizers of the functional.

Article information

Differential Integral Equations, Volume 28, Number 5/6 (2015), 401-430.

First available in Project Euclid: 30 March 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J75: Singular elliptic equations 35J25: Boundary value problems for second-order elliptic equations 35J66: Nonlinear boundary value problems for nonlinear elliptic equations 35B65: Smoothness and regularity of solutions 35J92: Quasilinear elliptic equations with p-Laplacian


Mazón, José M.; Rossi, Julio D.; de León, Sergio Segura. The $1$--Laplacian elliptic equation with inhomogeneous Robin boundary conditions. Differential Integral Equations 28 (2015), no. 5/6, 401--430. https://projecteuclid.org/euclid.die/1427744095

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