Заседание семинара РМЦ ЮФУ

В рамках еженедельного научно-​исследовательского семинара по анализу, дифференциальным уравнениям и математической физике РМЦ ЮФУ 27 сентября с 15:30 – 17:00 в ауд. 212 состоится лекция Briceyda B. Del­gado «Div-​Curl Sys­tem and consequences».

Приглашаются преподаватели, научные сотрудники, аспиранты, студенты и все желающие. e-​mail: Этот адрес электронной почты защищён от спам-​ботов. У вас должен быть включен JavaScript для просмотра..

Regional math­e­mat­i­cal cen­ter of South­ern Fed­eral Uni­ver­sity is pleased to invite you to the Sem­i­nar on analy­sis, dif­fer­en­tial equa­tions and math­e­mat­i­cal physics, which will be held on 27 Sep­tem­ber 2018 at 15:30 in the room 212.

The title of the lec­ture: Div-​Curl Sys­tem and con­se­quences. Lec­turer: Briceyda B. Delgado.

Abstract: In this talk we will recall some prop­er­ties of the non-​commutative alge­bra of quater­nions and some fun­da­men­tal prop­er­ties of the Teodor­escu trans­form, which was fun­da­men­tal for the solu­tion of the div-​curl sys­tem in star-​shaped domains.

Now we will give a weak solu­tion to the div-​curl sys­tem in bounded Lip­schitz domain in R³ [2], this allows us to con­sider more gen­eral domains with weaker topo­log­i­cal constraints.

Some appli­ca­tions of this solu­tion are to the main Vekua equa­tion and to the sta­tic Maxwell’s equa­tions with vari­able per­me­abil­ity [1].

In the con­struc­tion of the solu­tion to the div-​curl sys­tem besides of the com­po­nents oper­a­tors of the clas­si­cal Teodor­escu trans­form [1] are involved other layer poten­tial oper­a­tors related with clas­si­cal Dirich­let prob­lems [3].

[1] B. B. Del­gado, R. M. Porter, “Gen­eral solu­tion of the inho­mo­ge­neous div– curl sys­tem and con­se­quences,” Advances in Applied Clif­ford Alge­bras (2017) 3015 – 3037.

[2] B. B. Del­gado, R. M. Porter, “Hilbert trans­form for the three-​dimensional Vekua equa­tion,” https://​arxiv​.org/​p​d​f​/​1​8​0​3​.​0​3​2​9​3​.​p​d​f (2018).

[3] C. E. Kenig, Har­monic Analy­sis Tech­niques for Sec­ond Order Ellip­tic Bound­ary Value Prob­lems. CBMS Regional Con­fer­ence Series in Math­e­mat­ics, Num­ber 83, Amer­i­can Math­e­mat­i­cal Soci­ety, Rhode Island (1994).

[4] B. B. Del­gado, R. M. Porter, “Gen­eral solu­tion of the inho­mo­ge­neous div– curl sys­tem and con­se­quences,” Advances in Applied Clif­ford Alge­bras (2017) 3015 – 3037.
[5] K. Gür­lebeck, K. Habetha, W. Sprößig, Holo­mor­phic Func­tions in the Plane and n-​dimensional Space. Birkhäuser, Basel (2008).