In this paper we deal with a Dirichlet problem for an elliptic equation involving the 1-Laplace operator. Under suitable assumptions on the nonlinearity we show that there exists a symmetric, monotonic and positive solution via the moving plane method. We shall show a priori estimates for some positive solutions.
Citation: Lin Zhao. Monotonicity and symmetry of positive solution for 1-Laplace equation[J]. AIMS Mathematics, 2021, 6(6): 6255-6277. doi: 10.3934/math.2021367
In this paper we deal with a Dirichlet problem for an elliptic equation involving the 1-Laplace operator. Under suitable assumptions on the nonlinearity we show that there exists a symmetric, monotonic and positive solution via the moving plane method. We shall show a priori estimates for some positive solutions.
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Lin Zhao. Monotonicity and symmetry of positive solution for 1-Laplace equation[J]. AIMS Mathematics, 2021, 6(6): 6255-6277. doi: 10.3934/math.2021367
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