A proof of the inverse function theorem
A relaxation result in BV for integral functionals with discontinuous integrands
We prove a relaxation theorem in BV for a non coercive functional with linear growth. No continuity of the integrand with respect to the spatial variable is assumed.
A remark on functions continuous on all lines
We prove that each linearly continuous function on (i.e., each function continuous on all lines) belongs to the first Baire class, which answers a problem formulated by K. C. Ciesielski and D. Miller (2016). The same result holds also for on an arbitrary Banach space , if has moreover the Baire property. We also prove (extending a known finite-dimensional result) that such on a separable is continuous at all points outside a first category set which is also null in any usual sense.
A remark on -harmonic functions on Riemannian manifolds.
A remark on linear functions on the sphere
A remark on the compactness for the Cahn–Hilliard functional
In this note we prove compactness for the Cahn–Hilliard functional without assuming coercivity of the multi-well potential.
A Riemann-type definition for the double Denjoy integral of Chelidze and Djvarsheishvili
We give a Riemann-type definition of the double Denjoy integral of Chelidze and Djvarsheishvili using the new concept of filtering.
A sandwich with convexity for set-valued functions.
A selection theorem of Helly type and its applications
We prove an abstract selection theorem for set-valued mappings with compact convex values in a normed space. Some special cases of this result as well as its applications to separation theory and Hyers-Ulam stability of affine functions are also given.
A simple proof of the minimax-theorem
A simple proof of the Rademacher theorem
A simplified multidimensional integral
We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.
A spherical representation of the real directional derivative.
A strongly nonlinear problem arising in glaciology
The computation of glacier movements leads to a system of nonlinear partial differential equations. The existence and uniqueness of a weak solution is established by using the calculus of variations. A discretization by the finite element method is done. The solution of the discrete problem is proved to be convergent to the exact solution. A first simple numerical algorithm is proposed and its convergence numerically studied.
A Synopsis of Elementary Results in Pure Mathematics [Book]
A theorem about Carathéodory's superposition
A theorem of the alternative and a two-function minimax theorem.
A theory of non-absolutely convergent integrals in Rn with singularities on a regular boundary
Specializing a recently developed axiomatic theory of non-absolutely convergent integrals in , we are led to an integration process over quite general sets with a regular boundary. The integral enjoys all the usual properties and yields the divergence theorem for vector-valued functions with singularities in a most general form.
A version of Hilbert's 13th problem for infinitely differentiable functions.
About a man and lions