Decay estimates and a vanishing phenomenon for the solutions of critical anisotropic equations

作者：Vetois Jerome^*

来源：Advances in Mathematics, 2015, 284: 122-158.

DOI：10.1016/j.aim.2015.04.029

• Anisotropic equations
• Critical exponent
• Pointwise a priori estimates
• Anisotropic Sobolev inequality

We investigate the asymptotic behavior of solutions of anisotropic equations of the form - Sigma(n)(i=1) partial derivative(xi) (vertical bar partial derivative(xi)u vertical bar(pi-2) partial derivative(xi)u) = f (x, u) in R-n, where p(i) > 1 for all i = 1, ..., n and f is a Caratheodory function with critical Sobolev growth. This problem arises in particular from the study of extremal functions for a class of anisotropic Sobolev inequalities. We establish decay estimates for the solutions and their derivatives, and we bring to light a vanishing phenomenon which occurs when the maximum value of the pi exceeds a critical value.

• 出版日期2015-10-22
• 单位McGill