본문 바로가기
KERD
논문KCI 등재

GLOBAL Wp1,2 ESTIMATES FOR NONDIVERGENCE PARABOLIC OPERATORS WITH POTENTIALS SATISFYING A REVERSE HOLDER CONDITION

Lin Tang|Guixia Pan
대한수학회 (The Korean Mathematical Society)|2017.09|대한수학회지 (Journal of the KMS)|제54권 제5호|pp. 1357-1377

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

BMOparabolic operatorreverse H\"{o}lder conditionVMO
주제분류수학

초록

In this article, we first give the $L^{p}$ boundedness of the operator $D^{2}L^{-1}$ with BMO coefficients and a potential $V$ satisfying an appropriate reverse H\"{o}lder condition, then obtain global $W^{1,2}_p$ estimates for the nondivergence parabolic operator $L$ with VMO coefficients and a potential $V$ satisfying an appropriate reverse H\"{o}lder condition.

Abstract

In this article, we first give the $L^{p}$ boundedness of the operator $D^{2}L^{-1}$ with BMO coefficients and a potential $V$ satisfying an appropriate reverse H\"{o}lder condition, then obtain global $W^{1,2}_p$ estimates for the nondivergence parabolic operator $L$ with VMO coefficients and a potential $V$ satisfying an appropriate reverse H\"{o}lder condition.

참고문헌 (18)

  1. M. Bramanti, "Global W2,p estimates for nondivergence elliptic operators with potentials satisfying a reverse Holder condition", Ann. Mat. Pura Appl. (4), 191(2), pp.339~362 (2012)
  2. M. Bramanti, "W1,2p solvability for the Cauchy-Dirichlet problem for parabolic equations with VMO coefficients", Comm. Partial Differential Equations, 18(9-10), pp.1735~1763 (1993)
  3. N. Burger, "Espace des fonctions a variation moyenne bournee sur un espace de nature homogene", C. R. Acad. Sci. Paris Ser. A-B, 286(3), pp.139~142 (1978)
  4. A. Carbonaro, "Parabolic Schrodinger operators", J. Math. Anal. Appl, 343(2), pp.965~974 (2008)
  5. F. Chiarenza, "Interior W2,p estimates for nondivergence elliptic equations with discontinuous coefficients", Ricerche Mat, 40(1), pp.149~168 (1991)
  6. F. Chiarenza, "W2,p solvability of the Dirichlet problem for non divergence elliptic equations with VMO coefficents", Trans. Amer. Math. Soc, 336(2), pp.841~853 (1993)
  7. D. Gilbarg, "Elliptic Partial Differential Equations of Second Order" (1983), Springer-Verlag
  8. W. Gao, "Lp estimate for parabolic Schrodinger operator with certain potentials", J. Math. Anal. Appl, 310(1), pp.128~143 (2005)
  9. K. Kurata, "An estimate on the heat kernel of magnetic Schrodinger operators and uniformly elliptic operators with non-negative potentials", J. London Math. Soc, 62(3), pp.885~903 (2000)
  10. G. Lieberman, "Second Order Parabolic Differential Equations" (1996), World Scientific Publishing Co., Inc
  11. B. Muckenhoupt, "Weighted norm inequalities for the Hardy maximal function", Trans. Amer. Math. Soc, 165, pp.207~226 (1972)
  12. G. Pan, "Solvability for Schrodinger equations with discontinuous coefficients", J. Funct. Anal, 270(1), pp.88~133 (2016)
  13. Z. W. Shen, "On the Neumann problem for Schrodinger operators in Lipschitz domains", Indiana Univ. Math. J, 453(1), pp.143~176 (1994)
  14. Z. W. Shen, "Lp estimates for Schrodinger operators with certain potentials", Ann. Inst. Fourier (Grenoble), 45(2), pp.513~546 (1995)
  15. E. M. Stein, "Harmonic analysis: real variable methods orthogonality and oscillatory integrals" (1993), Princeton Univ. Press
  16. L. Tang, "Weighted Lp solvability for parabolic equations with partially BMO coefficients and its applications", J. Aust. Math. Soc, 96(4), pp.396~428 (2014)
  17. L. Tang, "Lp boundedness for parabolic Schrodinger type operators with certain nonnegative potentials", Forum Math, 23(1), pp.161~179 (2011)
  18. C. Vitanza, "A new contribution to the W2,p regularity for a class of elliptic second order equations with discontinuous coefficients", Matematiche (Catania), 48(2), pp.287~296 (1993)

관련 논문AI추천

Boundedness and compactness of commutators related with uniformly parabolic operatorsHonglei Shi, Kai Zhao, Shujuan Zhou대한수학회 · 대한수학회보2025 · 제62권 제4호Gradient estimates for elliptic equations in divergence form with partial Dini mean oscillation coefficients김세익, 최종근, Kyungrok Lee대한수학회 · 대한수학회지2020 · 제57권 제6호LOCAL CALDERO ́N-ZYGMUND ESTIMATES FOR PARABOLIC EQUATIONS WITH DUAL DATA이미경영남수학회 · East Asian Mathematical Journal2023 · 제39권 제1호Conormal derivative problem for elliptic equations in divergence form with partial Dini mean oscillation coefficients최종근강원경기수학회 · 한국수학논문집2020 · 제28권 제4호Global weak Morrey estimates for some Ultraparabolic operators of Kolmogorov-Fokker-Planck typeMaochun Zhu, Pengcheng Niu, Xiaojing Feng대한수학회 · 대한수학회보2014 · 제51권 제5호Global regularity of solutions to quasilinear conormal derivative problem with controlled growth김도윤대한수학회 · 대한수학회지2012 · 제49권 제6호

이 간행물의 다른 논문 (13건)

HILBERT FUNCTIONS OF STANDARD k-ALGEBRAS DEFINED BY SKEW-SYMMETRIZABLE MATRICES강오진pp. 1379-1410CLASSIFICATION OF FREE ACTIONS OF FINITE GROUPS ON 3-DIMENSIONAL NILMANIFOLDS구대환, 신준국, 오명성pp. 1411-1440ALMOST EINSTEIN MANIFOLDS WITH CIRCULANT STRUCTURESIva Dokuzovapp. 1441-1456FOXBY EQUIVALENCE RELATIVE TO C-WEAK INJECTIVE AND C-WEAK FLAT MODULESTiwei Zhao, Zenghui Gaopp. 1457-1482THE NAVIER-STOKES EQUATIONS WITH INITIAL VALUES IN BESOV SPACES OF TYPE B-1q,∞+3/qPen-Yuan Hsu, Reinhard Farwig, Yoshikazu Gigapp. 1483-1504
원문 보기