Asymptotic analysis of a semilinear elliptic equation in highly oscillating thin domains

作者：Pereira Marcone Correa^*

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2016, 67(5): 134.

DOI：10.1007/s00033-016-0727-y

• Semilinear elliptic equations
• Upper semicontinuity
• Lower semicontinuity
• Thin domains

In this work we are interested in the asymptotic behavior of a family of solutions of a semilinear elliptic problem with homogeneous Neumann boundary condition defined in a two-dimensional bounded set which degenerates to the unit interval as a positive parameter epsilon goes to zero. Here we also allow that upper and lower boundaries from this singular region present highly oscillatory behavior with different orders and variable profile. Combining results from linear homogenization theory and nonlinear analyzes we get the limit problem showing upper and lower semicontinuity of the solutions at epsilon = 0.

• 出版日期2016-10