Thibault Lacombe

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math.AP2026

Average gradient localisation for degenerate elliptic equations in the plane

Thibault Lacombe

We consider Lipschitz solutions to the possibly highly degenerate elliptic equation $div G (\nabla u) = 0$ in $B_{1} \subset R^{2}$ , for any continuous strictly monotone ve…

math.AP2024

On $C^{1}$ regularity for degenerate elliptic equations in the plane

Thibault Lacombe, Xavier Lamy

We show that Lipschitz solutions $u$ of $div G (\nabla u) = 0$ in $B_{1} \subset R^{2}$ are $C^{1}$ , for strictly monotone vector fields $G \in C^{0} (R^{2}; R^{2})$ …

Average gradient localisation for degenerate elliptic equations in the plane

On C1 regularity for degenerate elliptic equations in the plane

On $C^{1}$ regularity for degenerate elliptic equations in the plane