We study interior L p-regularity theory, also known as Calderon-Zygmund theory, of the
equation< L su, φ>:=∫ R n∫ R n K (x, y)(u (x)− u (y))(φ (x)− φ (y))| x− y| n+ 2 sdxdy=< f …

Given 2≤ p<∞, s∈(0, 1) and t∈(1, 2 s), we establish interior W t, p Calderón-Zygmund
estimates for solutions of nonlocal equations of the form∫ Ω∫ Ω K x,| xy|, xy| xy|(u (x)-u …

This paper addresses the approximation of fractional harmonic maps. Besides a unit-length
constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness …

We consider the problem of finding a surface Σ ⊂ R^ m Σ⊂ R m of least Willmore energy
among all immersed surfaces having the same boundary, boundary Gauss map and area …

We investigate minimizers and critical points for scale-invariant tangent-point energies TPp;
q of closed curves. We show that (a) minimizing sequences in ambient isotopy classes …

We prove that for antisymmetric vector field Ω with small L 2-norm there exists a gauge A∈
L∞∩ W˙ 1/2, 2 (R 1, GL (N)) such that div 1 2 (A Ω-d 1 2 A)= 0. This extends a celebrated …

In this article, we improve the partial regularity theory for minimizing 1/2-harmonic maps of
Millot and Sire (Arch Ration Mech Anal 215: 125–210, 2015), Moser (J Geom Anal 21: 588 …

Given $ p\geq 2$ and a map $ g: B^ n (0, 1)\to S_n^{++} $, where $ S_n^{++} $ is the group
of positively definite matrices, we study critical points of the following functional: $$ v\in …

We prove a priori estimates for wave systems of the type\[\partial_ {tt} u-\Delta
u=\Omega\cdot du+ F (u)\quad\text {in $\mathbb {R}^ d\times\mathbb {R} $}\] where $ d\geq …

arXiv:2402.04156v1 [math.AP] 6 Feb 2024 Page 1 arXiv:2402.04156v1 [math.AP] 6 Feb
2024 OPTIMAL WEIGHTED WENTE’S INEQUALITY MATILDE GIANOCCA Abstract. In this …