Recent zbMATH articles in MSC 31Bhttps://zbmath.org/atom/cc/31B2022-12-08T16:55:51.716093ZWerkzeugBoundary value problems for hypergenic function vectorshttps://zbmath.org/1497.300182022-12-08T16:55:51.716093Z"Zhang, Guiling"https://zbmath.org/authors/?q=ai:zhang.guiling"Li, Chong"https://zbmath.org/authors/?q=ai:li.chong.4|li.chong.1|li.chong.2|li.chong.5|li.chong.3"Xie, Yonghong"https://zbmath.org/authors/?q=ai:xie.yonghongSummary: This article mainly studies the boundary value problems for hypergenic function vectors in Clifford analysis. Firstly, some properties of hypergenic quasi-Cauchy type integrals are discussed. Then, by the Schauder fixed point theorem the existence of the solution to the nonlinear boundary value problem is proved. Finally, using the compression mapping principle the existence and uniqueness of the solution to the linear boundary value problem are proved.Convex sets and subharmonicity of the inverse norm functionhttps://zbmath.org/1497.310022022-12-08T16:55:51.716093Z"Heydari, Mohammad Taghi"https://zbmath.org/authors/?q=ai:heydari.mohammad-taghi(no abstract)A note on isolated removable singularities of harmonic functionshttps://zbmath.org/1497.310052022-12-08T16:55:51.716093Z"Srinivasan, Gopala Krishna"https://zbmath.org/authors/?q=ai:srinivasan.gopala-krishnaSummary: A proof of the removable singularities theorem for harmonic functions is presented which seems to be different from existing proofs in the literature. This is an important result in analysis with applications to many areas of mathematics. Weyl's lemma which is used in the course of the argument is also proved in a special case to make the note self-contained.
For the entire collection see [Zbl 1492.26003].Inverse mean value property of metaharmonic functionshttps://zbmath.org/1497.351092022-12-08T16:55:51.716093Z"Kuznetsov, N."https://zbmath.org/authors/?q=ai:kuznetsov.n-t|kuznetsov.nikolay-v|kuznetsov.nikolay-germanovich|kuznetsov.n-o|kuznetsov.nikolai-s|kuznetsov.n-m|kuznetsov.n-yu|kuznetsov.n-p|kuznetsov.n-d|kuznetsov.nickolay|kuznetsov.n-n|kuznetsov.n-k|kuznetsov.nikolai-aleksandrovichSummary: A new analytical characterization of balls in the Euclidean space \(\mathbb{R}^m\) is obtained. Previous results of this kind involved either harmonic functions or solutions to the modified Helmholtz equation (both have positive fundamental solutions), whereas solutions to the Helmholtz equation are used here. This is achieved at the expense of a restriction imposed on the size of admissible domains -- a feature absent in the inverse mean value properties known previously.A mean-value theorem for a B-polyharmonic equationhttps://zbmath.org/1497.351662022-12-08T16:55:51.716093Z"Kipriyanova, N. I."https://zbmath.org/authors/?q=ai:kipriyanova.n-i(no abstract)Riesz potential estimates for problems with Orlicz growthhttps://zbmath.org/1497.352432022-12-08T16:55:51.716093Z"Xiong, Qi"https://zbmath.org/authors/?q=ai:xiong.qi"Zhang, Zhenqiu"https://zbmath.org/authors/?q=ai:zhang.zhenqiu"Ma, Lingwei"https://zbmath.org/authors/?q=ai:ma.lingweiSummary: In this paper, we consider the solutions of the non-homogeneous quasilinear elliptic equations with Dini-\textit{BMO} coefficients involving measure data. At first, we prove pointwise gradient estimates for solutions by Riesz potentials; as a consequence, we obtain the borderline gradient regularity and extend a classical theorem of Stein for Poisson equations. Then we establish oscillation estimates of solutions via Riesz potentials, and these yield Hölder continuity of solutions.An inverse problem on determining second order symmetric tensor for perturbed biharmonic operatorhttps://zbmath.org/1497.355112022-12-08T16:55:51.716093Z"Bhattacharyya, Sombuddha"https://zbmath.org/authors/?q=ai:bhattacharyya.sombuddha"Ghosh, Tuhin"https://zbmath.org/authors/?q=ai:ghosh.tuhinAuthors' abstract: This article offers a study of the Calderón type inverse problem of determining up to second order coefficients of higher order elliptic operators. Here we show that it is possible to determine an anisotropic second order perturbation given by a symmetric matrix, along with a first order perturbation given by a vector field and a zero-th order potential function inside a bounded domain, by measuring the Dirichlet to Neumann map of the perturbed biharmonic operator on the boundary of that domain.
Reviewer: Giovanni S. Alberti (Genova)The strong CP problem and higher-dimensional gauge theorieshttps://zbmath.org/1497.811192022-12-08T16:55:51.716093Z"Adachi, Yuki"https://zbmath.org/authors/?q=ai:adachi.yuki"Lim, C. S."https://zbmath.org/authors/?q=ai:lim.cheol-su|lim.chia-s|lim.chee-seng"Maru, Nobuhito"https://zbmath.org/authors/?q=ai:maru.nobuhitoSummary: We discuss a natural scenario to solve the strong CP problem in the framework of the higher-dimensional gauge theory. An axion-like field \(A_y\) has been built in as the extra-space component of the higher-dimensional gauge field. The coupling of \(A_y\) with gluons is attributed to the radiatively induced ``Chern-Simons'' (CS) term. We adopt a toy model with some unknown gauge symmetry \(U(1)_{\mathrm{X}}\). The CS term is obtained in two ways: first by a concrete 1-loop calculation and next by use of Fujikawa's method to deal with the chiral anomaly in 4D space-time. The obtained results are identical, which implies that the radiative correction to the CS term is ``1-loop exact'' and is also free from UV-divergence even though the theory itself is non-renormalizable. As a novel feature of this scenario, the thus-obtained CS term is no longer linear in the field \(A_y\) as in the usually discussed CS term in 5D space-time but is a periodic function of \(A_y\), since \(A_y\) has a physical meaning as the Wilson-loop phase. We argue how such a novel feature in this scenario causes modification of the ordinary solutions of the strong CP problem based on the axion fields.