Fully nonlinear elliptic PDEs in thin domains with oblique boundary condition

Abstract

In this preprint we consider fully nonlinear equations in thin domains with oblique boundary condition, finding some new phenomena, in particular the limit equation contains "new terms" of the second, first and zeroth order which don't have an equivalent in the Neumann case treated in our previous work arXiv:2404.19577. The classical laplacian problem with Neumann boundary condition, goes back to the well known result of Hale and Raugel (1992).

Theorems & Definitions (25)

• Proposition 1
• Theorem 1
• Proposition 2
• Lemma 2
• proof
• Remark 3
• Proposition 4
• Lemma 3
• proof : Proof of Proposition \ref{['equivalenza']}
• proof : Proof of Lemma \ref{['maximum']}