Abstract 5

We consider multidimensional periodic structures, which can be identified with a periodic positive measure μ on Rⁿ. Using the concept of tangential calculus with respect to measures and related Sobolev spaces H^1,p(Ω,dμ), we study the homogenization of nonlinear elliptic equations

where ε>0 is the microscale parameter and μ_ε :=εⁿ μ(^⋅/_ε) are the rescaled measures. In case infinitely thin structures are fattened with another parameter δ, we also investigate the commutativity of the limit processes ε,δ → 0.

	Philip Heuser
	Homogenization of multidimentional structures

We consider multidimensional periodic structures, which can be identified with a periodic positive measure μ on Rⁿ. Using the concept of tangential calculus with respect to measures and related Sobolev spaces H^1,p(Ω,dμ), we study the homogenization of nonlinear elliptic equations where ε>0 is the microscale parameter and μ_ε :=εⁿ μ(^⋅/_ε) are the rescaled measures. In case infinitely thin structures are fattened with another parameter δ, we also investigate the commutativity of the limit processes ε,δ → 0.