대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제60권2호
  • /
  • Pages.495-505
  • /
  • 2023
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

A NOTE ON COMPARISON PRINCIPLE FOR ELLIPTIC OBSTACLE PROBLEMS WITH L1-DATA

  • Kyeong Song (Department of Mathematical Sciences Seoul National University) ;
  • Yeonghun Youn (Department of Mathematics Yeungnam University)
  • 투고 : 2022.04.06
  • 심사 : 2022.05.25
  • 발행 : 2023.03.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this note, we study a comparison principle for elliptic obstacle problems of p-Laplacian type with L1-data. As a consequence, we improve some known regularity results for obstacle problems with zero Dirichlet boundary conditions.

키워드

과제정보

This work was supported by NRF-2020R1C1C1A01009760.

참고문헌

  1. S. Baasandorj and S.-S. Byun, Irregular obstacle problems for Orlicz double phase, J. Math. Anal. Appl. 507 (2022), no. 1, Paper No. 125791, 21 pp. https://doi.org/10.1016/j.jmaa.2021.125791 
  2. P. Benilan, L. Boccardo, T. Gallouet, R. Gariepy, M. Pierre, and J. L. Vazquez, An L1-theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 22 (1995), no. 2, 241-273. 
  3. L. Boccardo and T. Gallouet, Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal. 87 (1989), no. 1, 149-169. https://doi.org/10.1016/0022-1236(89)90005-0 
  4. V. Bogelein, F. Duzaar, and G. Mingione, Degenerate problems with irregular obstacles, J. Reine Angew. Math. 650 (2011), 107-160. https://doi.org/10.1515/CRELLE.2011.006 
  5. S.-S. Byun, Y. Cho, and J. Ok, Global gradient estimates for nonlinear obstacle problems with nonstandard growth, Forum Math. 28 (2016), no. 4, 729-747. https://doi.org/10.1515/forum-2014-0153 
  6. S.-S. Byun, Y. Cho, and J.-T. Park, Nonlinear gradient estimates for elliptic double obstacle problems with measure data, J. Differential Equations 293 (2021), 249-281. https://doi.org/10.1016/j.jde.2021.05.035 
  7. S.-S. Byun, Y. Cho, and L. Wang, Calderon-Zygmund theory for nonlinear elliptic problems with irregular obstacles, J. Funct. Anal. 263 (2012), no. 10, 3117-3143. https://doi.org/10.1016/j.jfa.2012.07.018 
  8. S.-S. Byun, N. Cho, and Y. Youn, Existence and regularity of solutions for nonlinear measure data problems with general growth, Calc. Var. Partial Differential Equations 60 (2021), no. 2, Paper No. 80, 26 pp. https://doi.org/10.1007/s00526-020-01910-6 
  9. S.-S. Byun, J. Ok, and J.-T. Park, Regularity estimates for quasilinear elliptic equations with variable growth involving measure data, Ann. Inst. H. Poincare C Anal. Non Lineaire 34 (2017), no. 7, 1639-1667. https://doi.org/10.1016/j.anihpc.2016.12.002 
  10. S.-S. Byun and S. Ryu, Gradient estimates for nonlinear elliptic double obstacle problems, Nonlinear Anal. 194 (2020), 111333, 13 pp. https://doi.org/10.1016/j.na.2018.08.011 
  11. S.-S. Byun and K. Song, Maximal integrability for general elliptic problems with diffusive measures, Mediterr. J. Math. 19 (2022), no. 2, Paper No. 78, 20 pp. https://doi.org/10.1007/s00009-022-02014-5 
  12. S.-S. Byun, K. Song, and Y. Youn, Potential estimates for elliptic measure data problems with irregular obstacles, Preprint. 
  13. I. Chlebicka, A pocket guide to nonlinear differential equations in Musielak-Orlicz spaces, Nonlinear Anal. 175 (2018), 1-27. https://doi.org/10.1016/j.na.2018.05.003 
  14. L. Grafakos, Classical and Modern Fourier Analysis, Pearson Education, Inc., Upper Saddle River, NJ, 2004. 
  15. Y. Kim and S. Ryu, Elliptic obstacle problems with measurable nonlinearities in non-smooth domains, J. Korean Math. Soc. 56 (2019), no. 1, 239-263. https://doi.org/10.4134/JKMS.j180157 
  16. D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications, Pure and Applied Mathematics, 88, Academic Press, Inc., New York, 1980. 
  17. T. Kuusi and G. Mingione, Guide to nonlinear potential estimates, Bull. Math. Sci. 4 (2014), no. 1, 1-82. https://doi.org/10.1007/s13373-013-0048-9 
  18. G. Mingione, Gradient potential estimates, J. Eur. Math. Soc. (JEMS) 13 (2011), no. 2, 459-486. https://doi.org/10.4171/JEMS/258 
  19. G. Mingione and G. Palatucci, Developments and perspectives in nonlinear potential theory, Nonlinear Anal. 194 (2020), 111452, 17 pp. https://doi.org/10.1016/j.na.2019.02.006 
  20. J. F. Rodrigues and R. Teymurazyan, On the two obstacles problem in Orlicz-Sobolev spaces and applications, Complex Var. Elliptic Equ. 56 (2011), no. 7-9, 769-787. https://doi.org/10.1080/17476933.2010.505016 
  21. C. Scheven, Gradient potential estimates in non-linear elliptic obstacle problems with measure data, J. Funct. Anal. 262 (2012), no. 6, 2777-2832. https://doi.org/10.1016/j.jfa.2012.01.003 
  22. R. Servadei and E. Valdinoci, Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators, Rev. Mat. Iberoam. 29 (2013), no. 3, 1091-1126. https://doi.org/10.4171/RMI/750