Xavier Lamy

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20232026

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Showing 2024 · math.APShow all

3 papers · 2 filters

math.AP2024

On the existence of degenerate solutions of the two-dimensional $H$ -system

André Guerra, Xavier Lamy, Konstantinos Zemas

We consider entire solutions $ω \in H ˙^{1} (R^{2}; R^{3})$ of the $H$ -system $Δ ω = 2 ω_{x} \land ω_{y},$ which we refer to as bubbles. Surprisingly, and contrary to conjectures r…

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 $G \in C^{0} (R^{2}; R^{2})$ …

math.AP2024

On regularity and rigidity of $2 \times 2$ differential inclusions into non-elliptic curves

Xavier Lamy, Andrew Lorent, Guanying Peng

We study differential inclusions $D u \in Π$ in an open set $Ω \subset R^{2}$ , where $Π \subset R^{2 \times 2}$ is a compact connected $C^{2}$ curve without rank-one connecti…

On the existence of degenerate solutions of the two-dimensional H-system

On C1 regularity for degenerate elliptic equations in the plane

On regularity and rigidity of 2×2 differential inclusions into non-elliptic curves

On the existence of degenerate solutions of the two-dimensional $H$ -system

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

On regularity and rigidity of $2 \times 2$ differential inclusions into non-elliptic curves