본문 바로가기
KERD
논문KCI 등재

GLOBAL GRADIENT ESTIMATES FOR NONLINEAR ELLIPTIC EQUATIONS

유승진
대한수학회 (The Korean Mathematical Society)|2014.11|대한수학회지 (Journal of the KMS)|제51권 제6호|pp. 1209-1220

2

조회

0

다운로드

1

인용

0

참고문헌

키워드

BMO spacenonlinear elliptic equationglobal gradient estimateCalder´ on- Zygmund theoryReifenberg flat domain.
주제분류수학

초록

We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calder´ on-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

Abstract

We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calder´ on-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

참고문헌 (27)

  1. E. Acerbi, "Gradient estimates for a class of parabolic systems", Duke Math. J, 136(2), pp.285~320 (2007)
  2. P. Baroni, "Lorentz estimates for degenerate and singular evolutionary systems", J. Differential Equations, 255(9), pp.2927~2951 (2013)
  3. P. Baroni, "Global estimates for nonlinear parabolic equations", J. Evol. Equ, 13(1), pp.163~195 (2013)
  4. S. Byun, "Global gradient estimates for general nonlinear parabolic equations in nonsmooth domains", J. Differential Equations, 254(11), pp.4290~4326 (2013)
  5. S. Byun, "Weighted LP-estimates for elliptic equations with measurable coefficients in nonsmooth domains", Potential Anal, 41(1), pp.51~79 (2014)
  6. S. Byun, "Weighted W1,P estimates for solutions of non-linear parabolic equations over non-smooth domains", Bull. London Math. Soc, 45(4), pp.765~778 (2013)
  7. S. Byun, "Gradient estimates for higher order elliptic equations on nonsmooth domains", J. Differential Equations, 250(1), pp.243~263 (2011)
  8. S. Byun, "Global weighted estimates for the gradient of solutions to nonlinear elliptic equations", Ann. Inst. H. Poincare Anal. Non Lineaire, 30(2), pp.291~313 (2013)
  9. S. Byun, "Elliptic equations with BMO nonlinearity in Reifenberg domains", Adv. Math, 219(6), pp.1937~1971 (2008)
  10. L. A. Caffarelli, "On W¹,P estimates for elliptic equations in divergence form", Comm. Pure Appl. Math, 51(1), pp.1~21 (1998)
  11. H. Dong, "Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains", J. Funct. Anal, 261(11), pp.3279~3327 (2011)
  12. H. Dong, "LP solvability of divergence type parabolic and elliptic systems with partially BMO coefficients", Calc. Var. Partial Differential Equations, 40(3-4), pp.357~389 (2011)
  13. H. Dong, "The conormal derivative problem for higher order elliptic systems with irregular coefficients, Recent advances in harmonic analysis and partial differential equations", Contemp. Math, 581, pp.69~97 (2012)
  14. F. Duzaar, "Parabolic systems with polynomial growth and regularity", Mem. Amer. Math. Soc, 214(1005), pp.10~118 (2011)
  15. G. Di Fazio, "LP estimates for divergence form elliptic equations with discontinuous coefficients", Boll. Un. Mat. Ital A (7), 10(2), pp.409~420 (1996)
  16. A. Fiorenza, "Indices of Orlicz spaces and some applications", Comment. Math. Univ. Carolin, 38(3), pp.433~451 (1997)
  17. V. Kokilashvili, "Weighted Inequalities in Lorentz and Orlicz Spaces" (1991), World Scientific Publishing Co., Inc.
  18. N. V. Krylov, "Parabolic and elliptic equations with VMO coefficients", Comm. Partial Differential Equations, 32(1-3), pp.453~475 (2007)
  19. N. V. Krylov, "Lectures on elliptic and parabolic equations in Sobolev spaces" (2008), American Mathematical Society
  20. T. Mengesha, "Weighted and regularity estimates for nonlinear equations on Reifenberg flat domains", J. Differential Equations, 250(5), pp.2485~2507 (2011)
  21. T. Mengesha, "Global Estimates for quasilinear elliptic equations on Reifenberg flat domains", Arch. Ration. Mech. Anal, 203(1), pp.189~216 (2012)
  22. D. K. Palagachev, "A priori estimates and precise regularity for parabolic systems with discontinuous data", Discrete Contin. Dyn. Syst, 13(3), pp.721~742 (2005)
  23. N. C. Phuc, "Nonlinear Muckenhoupt-Wheeden type bounds on Reifenberg flat domains, with applications to quasilinear Riccati type equations", Adv. Math, 250, pp.387~419 (2014)
  24. L. G. Softova, "Morrey-type regularity of solutions to parabolic problems with discontinuous data", Manuscripta Math, 136(3-4), pp.365~382 (2011)
  25. T. Toro, "Doubling and flatness: geometry of measures", Notices Amer. Math. Soc, 44(9), pp.1087~1094 (1997)
  26. L. Wang, "Global regularity for higher order divergence elliptic and parabolic equations", J. Funct. Anal, 266(2), pp.792~813 (2014)
  27. L.Wang, "Optimal regularity theory for the Poisson equation", Proc. Amer. Math. Soc, 137(6), pp.2037~2047 (2009)

관련 논문AI추천

Elliptic obstacle problems with measurable nonlinearities in non-smooth domains김유찬, 유승진대한수학회 · 대한수학회지2019 · 제56권 제1호Global regularity of solutions to quasilinear conormal derivative problem with controlled growth김도윤대한수학회 · 대한수학회지2012 · 제49권 제6호Gradient estimates for elliptic equations in divergence form with partial Dini mean oscillation coefficients김세익, 최종근, Kyungrok Lee대한수학회 · 대한수학회지2020 · 제57권 제6호Conormal derivative problem for elliptic equations in divergence form with partial Dini mean oscillation coefficients최종근강원경기수학회 · 한국수학논문집2020 · 제28권 제4호LOCAL CALDERO ́N-ZYGMUND ESTIMATES FOR PARABOLIC EQUATIONS WITH DUAL DATA이미경영남수학회 · East Asian Mathematical Journal2023 · 제39권 제1호Weighted estimates for nonlinear equations of differential forms이미경영남수학회 · East Asian Mathematical Journal2025 · 제41권 제1호

이 간행물의 다른 논문 (12건)

BIHARMONIC CURVES IN FINSLER SPACESNicoleta Voicupp. 1105-1122UPPER AND LOWER SOLUTION METHOD FOR FRACTIONAL EVOLUTION EQUATIONS WITH ORDER 1 < α < 2Fei Xu, Xiao-Bao Shupp. 1123-1139PANCYCLIC ARCS IN HAMILTONIAN CYCLES OF HYPERTOURNAMENTSMichel Surmacs, Yubao Guopp. 1141-1154A UNIFIED CONVERGENCE ANALYSIS FOR SECANT-TYPE METHODSAngel Alberto Magrenan, Ioannis Konstantinos Argyrospp. 1155-1175ABSOLUTELY PURE REPRESENTATIONS OF QUIVERSMansour Aghasi, Hamidreza Nematipp. 1177-1187
원문 보기