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Non-relativistic model of the laws of gravity and electromagnetism, invariant under the change of inertial and non-inertial coordinate systems
Full text linkUnder the classical non-relativistic consideration of the space-time we propose the model of the laws of gravity and Electrodynamics, invariant under the galilean transformations and moreover, under every change of non-inertial cartesian coordinate system. Being in the frames of non-relativistic model of the space-time, we adopt some general ideas of the General Theory of Relativity, like the assumption of invariance of the most general physical laws in every inertial and non-inertial coordinate system and equivalence of factious forces in non-inertial coordinate systems and the force of gravity. Moreover, in the frames of our model, we obtain that the laws of Non-relativistic Quantum Mechanics also invariant under the change of inertial or non-inertial cartesian coordinate system.This is a preprint of the following work: Arkady Poliakovsky, The Laws of Gravity and Electromagnetism: A Non-relativistic Model Invariant Under the Change of Inertial and Non-inertial Coordinate Systems , 2024, Springer Cham, reproduced with permission of Springer Nature Switzerland AG 2024. The final authenticated version is available online at: https://doi.org/10.1007/978-3-031-61407-
On the Γ-limit of singular perturbation problems with optimal profiles which are not one-dimensional. Part II: The lower bound
No full text
Jump detection in Besov spaces via a new BBM formula. Applications to Aviles–Giga-type functionals
No full text Motivated by the formula, due to Bourgain, Brezis and Mironescu, [Formula: see text] that characterizes the functions in [Formula: see text] that belong to [Formula: see text] (for [Formula: see text]) and [Formula: see text] (for [Formula: see text]), respectively, we study what happens when one replaces the denominator in the expression above by [Formula: see text]. It turns out that for [Formula: see text] the corresponding functionals “see” only the jumps of the [Formula: see text] function. We further identify the function space relevant to the study of these functionals, the space [Formula: see text], as the Besov space [Formula: see text]. We show, among other things, that [Formula: see text] contains both the spaces [Formula: see text] and [Formula: see text]. We also present applications to the study of singular perturbation problems of Aviles–Giga type. </jats:p
Asymptotic behavior of the
No full textMotivated by results of Figalli and Jerison [J. Funct. Anal. 266 (2014) 1685–1701] and Hernández [Pure Appl. Funct. Anal., Preprint https://arxiv.org/abs/1709.0826
Upper bounds for a class of energies containing a non-local term
No full textIn this paper we construct upper bounds for families of
functionals of the form
where Δ = div { u}. Particular cases of such functionals arise in
Micromagnetics. We also use our technique to construct upper bounds
for functionals that appear in a variational formulation of
the method of vanishing viscosity for conservation laws
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