HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Nonlinear boundary value problems relative to harmonic functions

Abstract : We study the problem of finding a function u verifying −∆u = 0 in Ω under the boundary condition ∂u ∂n + g(u) = µ on ∂Ω where Ω ⊂ R N is a smooth domain, n the normal unit outward vector to Ω, µ is a measure on ∂Ω and g a continuous nondecreasing function. We give sufficient condition on g for this problem to be solvable for any measure. When g(r) = |r| p−1 r, p > 1, we give conditions in order an isolated singularity on ∂Ω be removable. We also give capacitary conditions on a measure µ in order the problem with g(r) = |r| p−1 r to be solvable for some µ. We also study the isolated singularities of functions satisfying −∆u = 0 in Ω and ∂u ∂n + g(u) = 0 on ∂Ω \ {0}.
Document type :
Journal articles
Complete list of metadata

Cited literature [40 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02494933
Contributor : Laurent Veron Connect in order to contact the contributor
Submitted on : Friday, July 31, 2020 - 11:47:43 AM
Last modification on : Tuesday, January 11, 2022 - 5:56:11 PM

Files

Bouk-Ver-Art-13.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02494933, version 2
  • ARXIV : 2003.00871

Collections

Citation

Y Oussama Boukarabila, Laurent Veron. Nonlinear boundary value problems relative to harmonic functions. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2020, 201, pp.112090. ⟨hal-02494933v2⟩

Share

Metrics

Record views

70

Files downloads

36