22 citations · 77 across the 17 of their papers we have counts for
14 papers · 1 filter
On the effective sharp stability of the Faber-Krahn inequality
André Guerra, João Miguel Machado, João P. G. Ramos
We prove the sharp quantitative Faber--Krahn inequality with a computable dimensional constant, resolving a problem posed by Brasco and De Philippis~\cite[Open Problem~2]{brasco201…
Morrey's problem in and
Andrea Agazzi, Giuseppe Bruno, André Guerra +1
We find an explicit rank-one convex non-quasiconvex integrand in : to falsify the quasiconvexity inequality, we exhibit a map …
On the sharp Hölder exponent in the De Giorgi--Nash--Moser theory
André Guerra
We consider solutions of uniformly elliptic equations with measurable coefficients. We assume that the lowest eigenvalue of the coefficient matrix is at least and the larg…
Sharp quantitative stability of the Möbius group among sphere-valued maps in arbitrary dimension
André Guerra, Xavier Lamy, Konstantinos Zemas
In this work we prove a sharp quantitative form of Liouville's theorem, which asserts that, for all , the weakly conformal maps of with degree ar…
Automatic quasiconvexity of homogeneous isotropic rank-one convex integrands
André Guerra, Jan Kristensen
We consider the class of non-negative rank-one convex isotropic integrands on which are also positively -homogeneous. If we prove, condit…
Compensation phenomena for concentration effects via nonlinear elliptic estimates
André Guerra, Bogdan Raiţă, Matthew Schrecker
We study compensation phenomena for fields satisfying both a pointwise and a linear differential constraint. This effect takes the form of nonlinear elliptic estimates, where const…
Oscillations in wave map systems and homogenization of the Einstein equations in symmetry
André Guerra, Rita Teixeira da Costa
In 1989, Burnett conjectured that, under appropriate assumptions, the limit of highly oscillatory solutions to the Einstein vacuum equations is a solution of the Einstein--massless…
Energy minimisers with prescribed Jacobian
André Guerra, Lukas Koch, Sauli Lindberg
We study the symmetry and uniqueness of maps which minimise the -Dirichlet energy, under the constraint that their Jacobian is a given radially symmetric function . We find…
Nonlinear open mapping principles, with applications to the Jacobian equation and other scale-invariant PDEs
André Guerra, Lukas Koch, Sauli Lindberg
For a nonlinear operator satisfying certain structural assumptions, our main theorem states that the following claims are equivalent: i) is surjective, ii) is open at z…
The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces
André Guerra, Lukas Koch, Sauli Lindberg
We study existence and regularity of solutions to the Dirichlet problem for the prescribed Jacobian equation, , where is integrable and bounded away from zero. In…
Compensated compactness: continuity in optimal weak topologies
André Guerra, Bogdan Raiţă, Matthew R. I. Schrecker
For -homogeneous linear differential operators of constant rank, we study the implication in and $\mathcal{A} v_j\rightarrow \mathcal{A}…
Remarks on Ornstein's non-inequality in
Daniel Faraco, André Guerra
We give a very concise proof of Ornstein's non-inequality for first- and second-order operators in two dimensions. The proof just needs a two-dimensional laminate supported o…
Quasiconvexity, null Lagrangians, and Hardy space integrability under constant rank constraints
André Guerra, Bogdan Raiţă
We present a systematic treatment of the theory of Compensated Compactness under Murat's constant rank assumption. We give a short proof of a sharp weak lower semicontinuity result…
Extremal rank-one convex integrands and a conjecture of Šverák
André Guerra
We show that in order to decide whether a given probability measure is laminate it is enough to verify Jensen's inequality in the class of extremal non-negative rank-one convex int…