Variational Analysis In Sobolev And Bv Spaces Applications To Pdes And Optimization Mps Siam Series On Optimization -

W k , p ( Ω ) ↪ W j , q ( Ω ) for k > j and p > q

Variational analysis in Sobolev and BV spaces involves the study of optimization problems of the form:

Variational analysis in Sobolev and BV spaces has several applications in PDEs and optimization. For example, consider the following PDE:

− Δ u = f in Ω