Details

Autor(en) / Beteiligte

• Silva, E. D.
• Carvalho, M. L.
• de Albuquerque, J. C.

Titel

Revised regularity results for quasilinear elliptic problems driven by the Φ-Laplacian operator

Ist Teil von

• Manuscripta mathematica, 2020-03, Vol.161 (3-4), p.563-582

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2020

Link zum Volltext

Quelle

SpringerNature Journals

Beschreibungen/Notizen

• It is establish regularity results for weak solutions of quasilinear elliptic problems driven by the well known Φ -Laplacian operator given by - Δ Φ u = g ( x , u ) , in Ω , u = 0 , on ∂ Ω , where Δ Φ u : = div ( ϕ ( | ∇ u | ) ∇ u ) and Ω ⊂ R N , N ≥ 2 , is a bounded domain with smooth boundary ∂ Ω . Our work concerns on nonlinearities g which can be homogeneous or non-homogeneous. For the homogeneous case we consider an existence result together with a regularity result proving that any weak solution remains bounded. Furthermore, for the non-homogeneous case, the nonlinear term g can be subcritical or critical proving also that any weak solution is bounded. The proofs are based on Moser’s iteration in Orlicz and Orlicz-Sobolev spaces.