相关论文: Generalized Elliptic Integrals and the Legendre M-…
Associated Legendre functions of fractional degree appear in the solution of boundary value problems in wedges or in toroidal geometries, and elsewhere in applied mathematics. In the classical case when the degree is half an odd integer,…
We prove a duality theorem the computation of certain Bellman functions is usually based on. As a byproduct, we obtain sharp results about the norms of monotonic rearrangements. The main novelty of our approach is a special class of…
We use some general properties, presented in previous work, to evaluate special cases of integrals relating Rogers-Ramanujan continued fraction, eta function and elliptic integrals.
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind).…
The objective of this paper is to establish a connection between the problem of optimal regularity among solutions to elliptic PDEs with measurable coefficients and the Liouville property at infinity. Initially, we address the…
On a smooth, closed Riemannian manifold, we study the question of proportionality of components, also called synchronization, of vector-valued solutions to nonlinear elliptic Schr\"odinger systems with constant coefficients. In particular,…
We present several theorems on strict and strong convexity, and higher order differential formulae for sandwiched quasi-relative entropy (a parametrised version of the classical fidelity). These are crucial for establishing global linear…
In this note we discuss some problems related to conformal slit-mappings. On the one hand, classical Loewner theory leads us to questions concerning the embedding of univalent functions into slit-like Loewner chains. On the other hand, a…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
The paper addresses questions of existence and regularity of solutions to linear partial differential equations whose coefficients are generalized functions or generalized constants in the sense of Colombeau. We introduce various new…
We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…
In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…
Motivared by Carleman's proof of the isoperimetric inequality in the plane, we study some sharp integral inequalities for harmonic functions on the upper halfspace. We also derive the regularity for nonnegative solutions of the associated…
It turns out that complex geodesics in Teichm\"uller spaces with respect to their invariant metrics are intrinsically connected with variational calculus for univalent functions. We describe this connection and show how geometric features…
We study functions on topometric spaces which are both (metrically) Lipschitz and (topologically) continuous, using them in contexts where, in classical topology, ordinary continuous functions are used. We study the relations of such…
The paper is devoted to the study, characterizations, and applications of variational convexity of functions, the property that has been recently introduced by Rockafellar together with its strong counterpart. First we show that these…
In the paper, we present a monotonicity result of a function involving the gamma function and the logarithmic function, refine a double inequality for the gamma function, and improve some known results for bounding the gamma function.
In recent works, arbitrary structural sets in the non-commutative Clifford analysis context have been used to introduce non-trivial generalizations of harmonic Clifford algebra valued functions in $\mathbb{R}^m$. Being defined as the…
We study anisotropic geometric energy functionals defined on a class of k-dimensional surfaces in a Euclidean space. The classical notion of ellipticity, coming from Almgren, for such functionals is investigated. We prove a variant of a…
We study the Schwarz lemma for harmonic functions and prove sharp versions for the cases of real harmonic functions and the norm of harmonic mappings.