A note on boundary differentiability of solutions of elliptic equations in nondivergence form

Huang, Yongpan; Li, Dongsheng; Wang, Lihe

doi:10.1007/s00229-019-01132-x

Cited by 5 publications

(2 citation statements)

References 17 publications

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“…In [4] Huang, Li and Wang proved that the solution of ( 3) is Lipschitz if the boundary satisfies exterior C 1,Dini condition and the solution is differentiable if the boundary is exterior C 1 Dini and punctually C 1 . Furthermore, in [5] they extended their results to Reifenberg C 1,Dini domain which is more general than the classical C 1,Dini domain. However, there are few results on the boundary behavior of solutions for semilinear elliptic equations in the divergence form.…”

Section: Introductionmentioning

confidence: 85%

Boundary Lipschitz regularity of solutions for semilinear elliptic equations in divergence form

Jingqi¹,

Wang²,

Zhou³

2021

Preprint

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In this paper, we consider the pointwise boundary Lipschitz regularity of solutions for the semilinear elliptic equations in divergence form mainly under some weaker assumptions on nonhomogeneous term and the boundary. If the domain satisfies C 1,Dini condition at a boundary point, and the nonhomogeneous term satisfies Dini continuous condition and Lipschitz Newtonian potential condition, then the solution is Lipschitz continuous at this point. Furthermore, we generalize this result to Reifenberg C 1,Dini domains.

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Section: Introductionmentioning

confidence: 85%

Boundary Lipschitz regularity of solutions for semilinear elliptic equations in divergence form

Jingqi¹,

Wang²,

Zhou³

2021

Preprint

Self Cite

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show abstract

“…In [5] and [6], Huang, Li and Wang got the boundary Lipschitz regularity under more general geometrical conditions, C 1,Dini condition or Reifenberg C 1,Dini condition. Furthermore if ∂Ω is punctually C 1 additionally, they obtained the boundary differentiability regularity.…”

Section: Introductionmentioning

confidence: 99%

Boundary Lipschitz regularity of solutions for general semilinear elliptic equations in divergence form

Liang¹,

Wang²,

Zhou³

2022

Preprint

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In this paper, we study the nonhomogeneous Dirichlet problem concerning general semilinear elliptic equations in divergence form. We establish that the boundary Lipschitz regularity of solutions under some more weaker conditions on the coefficients, the boundary, the boundary function and the nonhomogeneous term. In particular, we assume that the nonhomogeneous term satisfies Dini continuity condition and Lipschitz Newtonian potential condition, which will be the optimal conditions to obtain the boundary Lipschitz regularity of solutions.

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Pointwise boundary differentiability on Reifenberg domains for fully nonlinear elliptic equations

Niu

2021

manuscripta math.

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A note on boundary differentiability of solutions of elliptic equations in nondivergence form

Abstract: Boundary differentiability is shown for solutions of nondivergence elliptic equations with unbounded drift.

Cited by 5 publications

References 17 publications

Boundary Lipschitz regularity of solutions for semilinear elliptic equations in divergence form

Boundary Lipschitz regularity of solutions for semilinear elliptic equations in divergence form

Boundary Lipschitz regularity of solutions for general semilinear elliptic equations in divergence form

Pointwise boundary differentiability on Reifenberg domains for fully nonlinear elliptic equations

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