본문 바로가기
KERD
논문KCI 등재

Gradient type estimates for linear elliptic systems from composite materials

김유찬|신필수
대한수학회 (The Korean Mathematical Society)|2023.05|대한수학회지 (Journal of the KMS)|제60권 제3호|pp. 635-682|DOI 10.4134/JKMS.j220428

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

composite materialsLinear elliptic systemssmoothness and regularity
주제분류수학

초록

In this paper, we consider linear elliptic systems from composite materials where the coefficients depend on the shape and might have the discontinuity between the subregions. We derive a function which is related to the gradient of the weak solutions and which is not only locally piecewise H\"{o}lder continuous but locally H\"{o}lder continuous. The gradient of the weak solutions can be estimated by this derived function and we also prove the local piecewise gradient H\"{o}lder continuity which was obtained by the previous results.

Abstract

In this paper, we consider linear elliptic systems from composite materials where the coefficients depend on the shape and might have the discontinuity between the subregions. We derive a function which is related to the gradient of the weak solutions and which is not only locally piecewise H\"{o}lder continuous but locally H\"{o}lder continuous. The gradient of the weak solutions can be estimated by this derived function and we also prove the local piecewise gradient H\"{o}lder continuity which was obtained by the previous results.

참고문헌 (22)

  1. H. Ammari, "Gradient estimates for solutions to the conductivity problem", Math. Ann, 332(2), pp.277~286 (2005)[DOI]
  2. I. Babuˇska, "Damage analysis of fiber composites. I. Statistical analysis on fiber scale", Comput. Methods Appl. Mech. Engrg, 172(1-4), pp.27~77 (1999)[DOI]
  3. E. Bonnetier, "An elliptic regularity result for a composite medium with"touching"fibers of circular cross-section", SIAM J. Math. Anal, 31(3), pp.651~677 (2000)[DOI]
  4. S.-S. Byun, "Elliptic equations with measurable nonlinearities in nonsmooth domains", Adv. Math, 288, pp.152~200 (2016)[DOI]
  5. S.-S. Byun, "Elliptic equations with measurable coefficients in Reifenberg domains", Adv. Math, 225(5), pp.2648~2673 (2010)[DOI]
  6. H. Dong, "Gradient estimates for parabolic and elliptic systems from linear laminates", Arch. Ration. Mech. Anal, 205(1), pp.119~149 (2012)[DOI]
  7. H. Dong, "Parabolic and elliptic systems in divergence form with variably partially BMO coefficients", SIAM J. Math. Anal, 43(3), pp.1075~1098 (2011)[DOI]
  8. F. Duzaar, "Gradient estimates via non-linear potentials", Amer. J. Math, 133(4), pp.1093~1149 (2011)[DOI]
  9. Q. Han, "Elliptic partial differential equations" (2011), Courant Institute of Mathematical Sciences
  10. F. Hu, "Hessian estimates for fourth order elliptic systems with singular BMO coefficients in composite Reifenberg domains", J. Funct. Anal, 268(3), pp.555~584 (2015)[DOI]
  11. Y. Jang, "Global gradient estimates for parabolic systems from composite materials", Calc. Var. Partial Differential Equations, 57(2), pp.18~ (2018)[DOI]
  12. Y. Jang, "Gradient estimates for solutions of elliptic systems with measurable coefficients from composite material", Math. Methods Appl. Sci, 41(16), pp.7007~7031 (2018)[DOI]
  13. Y. Jang, "Global gradient estimates for nonlinear equations of p-Laplace type from composite materials", J. Math. Anal. Appl, 471(1-2), pp.1~14 (2019)[DOI]
  14. H. Kang, "Asymptotics and computation of the solution to the conductivity equation in the presence of adjacent inclusions with extreme conductivities", J. Math. Pures Appl, 99(2), pp.234~249 (2013)[DOI]
  15. Y. Kim, "Riesz potential type estimates for nonlinear elliptic equations", J. Differential Equations, 263(10), pp.6844~6884 (2017)[DOI]
  16. Y. Kim, "Piecewise smoothness for linear elliptic systems with piecewise smoothness coefficients, preprint", ~
  17. Y. Kim, "A geometric result for composite materials with C1,γ-boundaries, preprint", ~
  18. T. Kuusi, "Linear potentials in nonlinear potential theory", Arch. Ration. Mech. Anal, 207(1), pp.215~246 (2013)[DOI]
  19. Y. Li, "Estimates for elliptic systems from composite material", Comm. Pure Appl. Math, 56(7), pp.892~925 (2003)[DOI]
  20. Y. Li, "Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients", Arch. Ration. Mech. Anal, 153(2), pp.91~151 (2000)[DOI]
  21. K. W. Um, "Elliptic equations with singular BMO coefficients in Reifenberg domains", J. Differential Equations, 253(11), pp.2993~3015 (2012)[DOI]
  22. C. Zhang, "Gradient estimates for p-Laplacian equation in composite Reifenberg domains", Nonlinear Anal, 133, pp.134~143 (2016)[DOI]

관련 논문AI추천

Lipschitz regularity of homogenization with continuous coefficients: Dirichlet problem이성진대한수학회 · 대한수학회지2025 · 제62권 제4호Conormal derivative problem for elliptic equations in divergence form with partial Dini mean oscillation coefficients최종근강원경기수학회 · 한국수학논문집2020 · 제28권 제4호Gradient estimates for elliptic equations in divergence form with partial Dini mean oscillation coefficients김세익, 최종근, Kyungrok Lee대한수학회 · 대한수학회지2020 · 제57권 제6호GLOBAL GRADIENT ESTIMATES FOR NONLINEAR ELLIPTIC EQUATIONS유승진대한수학회 · 대한수학회지2014 · 제51권 제6호Elliptic 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 제6호

이 간행물의 다른 논문 (8건)

Symmetry of the twisted Gromov-Witten classes of projective line노현호pp. 479-501Schur convexity of $L$-conjugate means and its applicationsHUAN-NAN SHI, Dong-Sheng Wang, Chun-Ru Fupp. 503-520On uniformly $S$-absolutely pure modulesXiaolei Zhangpp. 521-536Two-sided estimates for transition probabilities of symmetric Markov chains on $\Z^d$Zhi-He Chenpp. 537-564On solvability of a class of degenerate Kirchhoff equations with logarithmic nonlinearityUgur Sertpp. 565-586
원문 보기