Large solutions for the elliptic $1$-Laplacian with absorption

Abstract

In this paper we give a general condition on the absorption term of the 1-Laplace elliptic equation for the existence of suitable large solutions. This condition can be considered as the correspondent Keller-Osserman condition for the $p$-Laplacian, in the case $p=1$. We also provide conditions that guarantee uniqueness for solutions to such problems.

References in corpus (2)

• Symmetry of large solutions of nonlinear elliptic equations in a ball
• Local estimates for parabolic equations with nonlinear gradient terms

Cited by in corpus (3)

• The Dirichlet problem for singular elliptic equations with general nonlinearities
• Nonlinear diffusion in transparent media: the resolvent equation
• 1-Laplacian type problems with strongly singular nonlinearities and gradient terms