Anisotropic Neumann problems in Sobolev spaces with variable exponent

作者：Boureanu Maria Magdalena; Radulescu Vicentiu D^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2012, 75(12): 4471-4482.

DOI：10.1016/j.na.2011.09.033

• Anisotropic Sobolev space
• Variable exponent
• Neumann elliptic problem
• Weak solutions
• Existence
• Uniqueness
• Trace theorem

We prove a trace theorem that allows the treatment of Neumann problems with nonlinearities on the boundary in anisotropic spaces with variable exponent. Then we proceed to the study of such a problem that involves general operators of the (p) over right arrow(.)-Laplace type. We deduce the existence of solutions and we direct attention to the situation where the solution is unique.

• 出版日期2012-8