The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …

Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with
smooth boundary, are not only of considerable intrinsic interest but have for many years …

The chemotaxis system\[\left\{\begin {array}{l} u_t=\Delta u-\chi\nabla\cdot (\frac {u}{v}\nabla
v), v_t=\Delta v-v+ u,\end {array}\right.\] is considered in a bounded domain $\Omega\subset …

Tearing and interconnecting methods, such as FETI, FETI-DP, BETI, etc., are among the
most successful domain decomposition solvers for partial differential equations. The …

This book discusses advances in maximal function methods related to Poincaré and
Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's …

In the theory for domain decomposition algorithms of the iterative substructuring family, each
subdomain is typically assumed to be the union of a few coarse triangles or tetrahedra. This …

The relationship between the operator norms of fractional integral operators acting on
weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds …

In the theory of domain decomposition methods, it is often assumed that each subdomain is
the union of a small set of coarse triangles or tetrahedra. In this study, extensions to the …

In an era marked by escalating environmental and social crises, transforming urban systems
is necessary. Currently, urban environments epitomise the degenerative impacts of …

We show how to use Lyapunov functions to obtain functional inequalities which are stronger
than Poincaré inequality (for instance logarithmic Sobolev or F-Sobolev). The case of …