Related papers: Generalized Elliptic Integrals and the Legendre M-…
The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far the method has not been proven to be able to handle extreme…
The inverse problem of linear elasticity is to determine the Lam\'e parameters, which characterize the mechanical properties of a domain, from pairs of pressure activations and the resulting displacements on its boundary. This work…
We use reflections involving analytic Dirichlet and Neumann data on a real-analytic curve in order to find a representation of solutions to Cauchy problems for harmonic functions in the plane. We apply this representation for finding…
We consider general linear non-degenerate weakly-coupled cooperative elliptic systems and study certain monotonicity properties of the generalized principal eigenvalue in $\mathbb{R}^d$ with respect to the potential. It is shown that…
On any metric space, I provide an intrinsic characterization of those complex-valued functions which are uniform limits of Lipschitz functions. There are applications to function theory on complete Riemannian manifolds and, in particular,…
The main thrust of our current work is to exploit very specific characteristics of a given problem in order to acquire improved compactness for supercritical problems and to prove existence of new types of solutions. To this end, we shall…
We study the homogenization of elliptic systems of equations in divergence form where the coefficients are compositions of periodic functions with a random diffeomorphism with stationary gradient. This is done in the spirit of scalar…
In discrete convex analysis, various convexity concepts are considered for discrete functions such as separable convexity, L-convexity, M-convexity, integral convexity, and multimodularity. These concepts of discrete convex functions are…
The Mittag-Leffler function plays an important role in Geometric Function Theory, particularly in the study of analytic and meromorphic function classes. Among its various generalizations, the Barnes-Mittag-Leffler function stands out due…
This is a survey of results mostly relating elliptic equations and systems of arbitrary even order with rough coefficients in Lipschitz graph domains. Asymptotic properties of solutions at a point of a Lipschitz boundary are also discussed.
In this paper we show that minima and stable solutions of a general energy functional of the form $$ \int_{\Omega} F(\nabla u,\nabla v,u,v,x)dx $$ enjoy some monotonicity properties, under an assumption on the growth at infinity of the…
We study counting functions of planar polygons arising from homological mirror symmetry of elliptic curves. We first analyze the signature and rationality of the quadratic forms corresponding to the signed areas of planar polygons. Then we…
We discuss elliptic quantum Calogero-Moser-Sutherland models, including their relativistic generalizations due to Ruijsenaars and van Diejen, and the relations of these models to classes of special functions developed and explored in recent…
In this note our aim is to deduce some new monotonicity properties for a special combination of Bessel functions of the first kind by using a recently developed Mittag-Leffler expansion for the derivative of a normalized Bessel function of…
The manuscript establishes a series expansion of the core integral that relates changes in longitude and latitude along the geodetic line in oblate elliptical coordinates, and of a companion integral which is the path length along this line…
In this paper, we establish some new integral inequalities for for m- and (alpha,m)-logarithmically convex functions.
We consider positive singular solutions to semilinear elliptic problems with possibly singular nonlinearity. We deduce symmetry and monotonicity properties of the solutions via the moving plane procedure.
We investigate the qualitative properties of positive solutions to mixed local-nonlocal equations with indefinite nonlinearities, emphasizing the interaction between classical and fractional Laplacians. We first establish maximum principles…
The conformal mapping problem for the section of a channel filled with porous material under a rectangular dam onto the upper half-plane is considered. Similar problems arise in computing of fluid flow in hydraulic structures. As a solution…
We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional…