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Boundary behavior of solutions of elliptic equations in nondivergence form

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Abstract

A new proof for boundary Lipschitz estimate is shown for solutions of elliptic equations in nondivergence form. Under additional condition, the boundary differentiability is obtained.

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References

  1. Caffarelli, L.A., Cabre, X.: Fully nonlinear elliptic equations. AMS 43, Providence, RI (1995)

  2. Gilbarg D., Trudinger N.S.: Elliptic Partial Differential Equations of Second Order. Springer, Berlin (1983)

    Book  MATH  Google Scholar 

  3. Krylov, N.V.: Boundedly inhomogeneous elliptic and parabolic equations in a domain. Izvestia Akad. Nauk. SSSR 47, 75–108 (1983) [Russian]. (English translation in Math. USSR Izv. 22, 67–97 (1984)

  4. Krylov, N.V.: On estimates for the derivatives of solutions of nonlinear parabolic equations. Dokl. Akad. Nauk. SSSR 274, 23–26 (1984) (Russian); English transl., Soviet Math. Dokl. 29, 14–17 (1984)

  5. Lieberman G.M.: The Dirichlet problem for quasilinear elliptic equations with continuously differentiable boundary data. Commun. Partial Differ. Equ. 11, 167–229 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  6. Li D., Wang L.: Boundary differentiability of solutions of elliptic equations on convex domains. Manuscr. Math. 121, 137–156 (2006)

    Article  MATH  Google Scholar 

  7. Li D., Wang L.: Elliptic equations on convex domains with nonhomogeneous Dirichlet boundary conditions. J. Differ. Equ. 246, 1723–1743 (2009)

    Article  MATH  Google Scholar 

  8. Ma F., Wang L.: Boundary first order derivatives estimates for fully nonlinear elliptic equations. J. Differ. Equ. 252, 988–1002 (2012)

    Article  MATH  Google Scholar 

  9. Safonov, M.V.:, Boundary estimates for positive solutions to second order elliptic equations. arXiv:0810.0522v2 [math.AP] 2 Oct 2008

  10. Wang L.: On the regularity theory of fully nonlinear parabolic equations: II. Commun. Pure Appl. Math. XLV, 141–178 (1992)

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Yongpan Huang & Dongsheng Li

  2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China

    Lihe Wang

  3. Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA

    Lihe Wang

Authors
  1. Yongpan Huang
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  2. Dongsheng Li
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  3. Lihe Wang
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Correspondence to Yongpan Huang.

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Huang, Y., Li, D. & Wang, L. Boundary behavior of solutions of elliptic equations in nondivergence form. manuscripta math. 143, 525–541 (2014). https://doi.org/10.1007/s00229-013-0643-9

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  • DOI: https://doi.org/10.1007/s00229-013-0643-9

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