On the Lipschitz character of orthotropic $p-$harmonic functions

Pierre Bousquet (1) , Lorenzo Brasco (2, 3) , Chiara Leone (4) , Anna Verde (4)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 DMCS - Dipartimento di Matematica e Informatica = Department of Mathematics and Computer Science [Ferrara]
3 I2M - Institut de Mathématiques de Marseille
4 Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”

We prove that local weak solutions of the orthotropic p−harmonic equation are locally Lipschitz, for every p ≥ 2 and in every dimension. More generally, the result holds true for more degenerate equations with orthotropic structure, with right-hand sides in suitable Sobolev spaces.

Mots clés: Degenerate elliptic equations; Anisotropic problems; Orthotropic problems; Sobolev spaces; Lipschitz regularity

Domaines: Equations aux dérivées partielles [math.AP]

Pierre Bousquet, Lorenzo Brasco, Chiara Leone, Anna Verde. On the Lipschitz character of orthotropic $p-$harmonic functions. Calculus of Variations and Partial Differential Equations, 2018, 57 (3), pp.88. ⟨10.1007/s00526-018-1349-3⟩. ⟨hal-01559511⟩