Abstract
Additive eigenvalue problem appears in ergodic optimal control or the homogenization of Hamilton–Jacobi equations. It has wide applications in several fields including computer science and then attracts the attention. In this paper, we consider the Poisson equations with the prescribed contact angle boundary condition and finally derive the existence and the uniqueness of the solution to the additive problem of the Laplace operator with the prescribed contact angle boundary condition.
Highlights
Additive eigenvalue problem appears in ergodic optimal control or the homogenization of Hamilton–Jacobi equations
As a character of large time behavior, it appears in the fields of computer science, big datadriven cloud service recommendation, etc
We consider the additive eigenvalue problem, and our main result is related to the additive eigenvalue problem of the Laplace operator with the prescribed contact angle boundary condition
Summary
Additive eigenvalue problem appears in ergodic optimal control or the homogenization of Hamilton–Jacobi equations. It is usually applied to study the large time behavior of the Cauchy problem of Hamilton–Jacobi equations. In [19], Xu derived the gradient estimate for Poisson equations with the prescribed contact angle boundary condition. We consider the additive eigenvalue problem, and our main result is related to the additive eigenvalue problem of the Laplace operator with the prescribed contact angle boundary condition.
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