Applicable Analysis wishes to become a leading journal for excellent papers on all mathematical aspects of Nonsmooth Variational Problems including new methods and techniques from Nonlinear and Nonsmooth Analysis. As a first step in this direction, the Editorial Board has decided to organize a special volume of the journal dedicated to this subject.
Nonsmooth Variational Problems have their origin in the study of nondifferentiable energy functionals, and they arise as necessary conditions of critical points of such functionals. In this way, variational inequalities are related with nonsmooth, convex energy functionals, whereas the so called hemivariational inequalities arise in the study of nonsmooth, nonconvex functionals that are, in general, merely locally Lipschitz. Just as the notion ‘nonlinear’ stands for ‘not necessarily linear’, we use the notion ‘nonsmooth’ to refer to ‘not neccesarily smooth’. The field of variational-hemivariational inequalities along with their corresponding evolutionary counterparts, initiated with the pioneering work of P.D. Panagiotopoulos, has attracted increasing attention over the last two decades mainly due to its many applications in mechanics and engineering. The study of such type of problems is closely related to the development of both theoretical and computational methods and techniques, such as, for example, a critical point theory for certain classes of nonsmooth functionals.
It is the hope of the Editorial Board that the current issue will encourage mathematicians to submit high quality papers to Applicable Analysis that focus on Nonsmooth Variational Problems in a wide sense to include, for example, boundary value problems with nonsmooth data under constraints such as multi-valued elliptic and evolutionary problems governed by multi-functions of Clarke's gradient type, as well as related variational-hemivariational inequalities.