Carleman formula for the Maxwell equation in a cap type domain

Komil O. Makhmudov

Department of Mechanics and Mathematics, University of Samarkand, University Boulevard, 15, Samarkand, 140104, Uzbekistan

Abstract: We consider a Cauchy problem for the Maxwell equations in a cap type domain $\mathcal{X}$ in $\mathbb{R}^3$. We find reasonable solvability conditions and a Carleman formula for its solution.

Keywords: Carleman formula, scattering, elliptic complex, Green formulas, Stratton–Chu formulas, Cauchy problem.

UDC: 517.5

Received: 28.01.2019
Received in revised form: 06.02.2019
Accepted: 06.03.2019

Language: English

DOI: 10.17516/1997-1397-2019-12-3-317--322