Related papers: Inverse problem in the calculus of variations -- f…
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical…
We have established a coherent framework for applying variational methods to partial differential equations on hypergraphs, which includes the propositions of calculus and function spaces on hypergraphs. Several results related to the…
In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic and nonrelativistic Newton equations in a static external electromagnetic field…
Problems in additive number theory related to sum and difference sets, more general binary linear forms, and representation functions of additive bases for the integers and nonnegative integers.
We present a novel approach to the Liouville problem for the stationary Navier-Stokes equations. As an application of our method, we prove conditional Liouville theorems with assumptions on the antiderivative of the velocity that represent…
Variational principles are proved for self-adjoint operator functions arising from variational evolution equations of the form \[ \langle\ddot{z}(t),y \rangle + \mathfrak{d}[\dot{z} (t), y] + \mathfrak{a}_0 [z(t),y] = 0. \] Here…
We review the multivariate holomorphic functional calculus for tuples in a commutative Banach algebra and establish a simple "na\"ive" extension to commuting tuples in a general Banach algebra. The approach is na\"ive in the sense that the…
This paper is concerned about the inverse coefficient problems of variable-coefficient fractional Schr\"{o}dinger equations with drift on connected closed Riemannian manifolds. We prove that the knowledge of the underlying equation of order…
The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in…
Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some…
Conformally invariant functionals on the space of knots are introduced via extrinsic conformal geometry of the knot and integral geometry on the space of spheres. Our functionals are expressed in terms of a complex-valued 2-form which can…
In this work, we consider boundary value problems involving Caputo and Riemann-Liouville fractional derivatives of order $\alpha\in(1,2)$ on the unit interval $(0,1)$. These fractional derivatives lead to non-symmetric boundary value…
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.
It is shown that the new formula for the field theory Poisson brackets arise naturally in the extension of the formal variational calculus incorporating divergences. The linear spaces of local functionals, evolutionary vector fields,…
This book aims to provide a brief overview of recent advancements in the theory of inverse problems for stochastic partial differential equations. In order to keep the content concise, we will only discuss the inverse problems of two…
The fractional Calder\'on problem asks to determine the unknown coefficients in a nonlocal, elliptic equation of fractional order from exterior measurements of its solutions. There has been substantial work on many aspects of this inverse…
We prove an implicit function theorem and an inverse function theorem for free noncommutative functions over operator spaces and on the set of nilpotent matrices. We apply these results to study dependence of the solution of the initial…
We outline an approach to the inverse problem of Calder\'on that highlights the role of microlocal normal forms and propagation of singularities and extends a number of earlier results also in the anisotropic case. The main result states…
The paper addresses the formulation and analysis of direct and inverse problems for a Langevin-type fractional differential equation under a non-local condition imposed on the time variable. An additional condition for solving the inverse…
We present the coisotropic embedding theorem as a tool to provide a solution for the inverse problem of the calculus of variations for a particular class of implicit differential equations, namely the equations of motion of free…