The field of variable exponent function spaces has witnessed an explosive growth in recent
years. The standard reference article for basic properties is already 20 years old. Thus this …

Analysis in spaces with no a priori smooth structure has progressed to include concepts from
the first order calculus. In particular, there have been important advances in understanding …

The $ p $-Laplace equation is the main prototype for nonlinear elliptic problems and forms a
basis for various applications, such as injection moulding of plastics, nonlinear elasticity …

There are several generalizations of the classical theory of Sobolev spaces as they are
necessary for the applications to Carnot-Caratheodory spaces, subelliptic equations …

This paper studies a possible de finition of Sobolev spaces in abstract metric spaces and
answers in the affi rmative the question whether this defi nition yields a Banach space. The …

In this survey we provide an overview of nonlinear elliptic homogeneous boundary value
problems featuring singular zero-order terms with respect to the unknown variable whose …

We describe recent theoretical and experimental progress on making objects invisible to
detection by electromagnetic waves. Ideas for devices that would once have seemed fanciful …

We describe new configurations of electromagnetic (EM) material parameters, the electric
permittivity ϵ and magnetic permeability μ, which allow one to construct devices that function …

Using the theory of Sobolev spaces on a metric measure space we are able to apply
calculus of variations and define p-harmonic functions as minimizers of the p-Dirichlet …

This paper explores a Dirichlet type problem on metric measure spaces. The problem is to
find a Sobolev-type function that minimizes the energy integral within a class of" Sobolev" …