Skip navigation

상단메뉴

글로벌메뉴

좌측메뉴

학술행사

검색

논문

tab menu

  • View
  • All
  • 수학부
  • 물리학부
  • 계산과학부
  • Center for Advanced Computation

Seminar View

Seminar
TITLE Carleman estimates and boundedness of associated multiplier operators
KIAS AUTHORS Kwon, Yehyun
JOURNAL COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2022
ARCHIVE https://arxiv.org/abs/1803.03040
ABSTRACT Let P(D) be the Laplacian Delta, or the wave operator square. The following type of Carleman estimate is known to be true on a certain range of p, q: parallel to e(v.x)u parallel to(Lq(Rd)) <= C parallel to e(v.x)P(D)u parallel to(Lp(Rd)) with C independent of v is an element of R-d. The estimates are consequences of the uniform Sobolev type estimates for second order differential operators due to Kenig-Ruiz-Sogge [1] and Jeong-Kwon-Lee [2]. The range of p, q for which the uniform Sobolev type estimates hold was completely characterized for the second order differential operators with nondegenerate principal part. But the optimal range of p, q for which the Carleman estimate holds has not been clarified before. When P(D) = Delta, square, or the heat operator, we obtain a complete characterization of the admissible p, q for the aforementioned type of Carleman estimate. For this purpose we investigate L-p-L-q boundedness of related multiplier operators. As applications, we also obtain some unique continuation results.
  • before page
  • list
  • next page
Seminar List

keyword

fiel&date

~