A uniqueness theorem is established for autonomous systems of ODEs, x= f(x), where f is a Sobolev vector field with additional geometric structure, such as delta-monoticity or reduced quasiconformality. Specifically, through every non-critical point of f there passes a unique integral curve
We introduce the definition of irreducible quasimodes, which are quasimodes with $h$-wavefront sets ...
For proving the existence and uniqueness of strong solutions to dY/dt = F(Y), Y(0) = C, the most quo...
AbstractThe paper treats functions which in a finite dimensional normed space over a field with a no...
A uniqueness theorem is established for autonomous systems of ODEs, x= f(x), where f is a Sobolev ve...
In this paper we provide a complete analogy between the Cauchy-Lipschitz and the DiPerna-Lions theo...
[[abstract]]Given an initial value problem. Its solution is called a semiflow,and forms an dynamical...
The seminal work of DiPerna and Lions (Invent Math 98(3):511–547, 1989) guarantees the existence and...
AbstractConditions are given for uniqueness of limit cycles for autonomous equations in the plane. T...
We construct divergence-free Sobolev vector fields in C([0, 1]; W 1,r (T d ; R d)) with r < d and d ...
AbstractWe consider the one-dimensional ordinary differential equation with a vector field which is ...
For solutions of ${\rm div}\,(DF(Du))=f$ we show that the quasiconformality of $z\mapsto DF(z)$ is t...
AbstractSuppose that f=(u,v) is a homeomorphism in the plane of the Sobolev class Wloc1,1 such that ...
We prove a Lipschitz extension lemma in which the extension procedure simultaneously preserves the L...
We provide a series of rigidity results for a nonlocal phase transition equation. The results that w...
We show that vector fields $b$ whose spatial derivative $D_xb$ satisfies a Orlicz summability condit...
We introduce the definition of irreducible quasimodes, which are quasimodes with $h$-wavefront sets ...
For proving the existence and uniqueness of strong solutions to dY/dt = F(Y), Y(0) = C, the most quo...
AbstractThe paper treats functions which in a finite dimensional normed space over a field with a no...
A uniqueness theorem is established for autonomous systems of ODEs, x= f(x), where f is a Sobolev ve...
In this paper we provide a complete analogy between the Cauchy-Lipschitz and the DiPerna-Lions theo...
[[abstract]]Given an initial value problem. Its solution is called a semiflow,and forms an dynamical...
The seminal work of DiPerna and Lions (Invent Math 98(3):511–547, 1989) guarantees the existence and...
AbstractConditions are given for uniqueness of limit cycles for autonomous equations in the plane. T...
We construct divergence-free Sobolev vector fields in C([0, 1]; W 1,r (T d ; R d)) with r < d and d ...
AbstractWe consider the one-dimensional ordinary differential equation with a vector field which is ...
For solutions of ${\rm div}\,(DF(Du))=f$ we show that the quasiconformality of $z\mapsto DF(z)$ is t...
AbstractSuppose that f=(u,v) is a homeomorphism in the plane of the Sobolev class Wloc1,1 such that ...
We prove a Lipschitz extension lemma in which the extension procedure simultaneously preserves the L...
We provide a series of rigidity results for a nonlocal phase transition equation. The results that w...
We show that vector fields $b$ whose spatial derivative $D_xb$ satisfies a Orlicz summability condit...
We introduce the definition of irreducible quasimodes, which are quasimodes with $h$-wavefront sets ...
For proving the existence and uniqueness of strong solutions to dY/dt = F(Y), Y(0) = C, the most quo...
AbstractThe paper treats functions which in a finite dimensional normed space over a field with a no...