Related papers: Weighted Low-Regularity Solutions of the KP-I Init…
In this paper we prove full local well-posedness for the Cauchy problem for the compressible 3D Euler equation, i.e. local existence, uniqueness, and continuous dependence on initial data, with initial velocity, density and vorticity…
A pointwise bound for local weak solutions to the p-Laplace system is established in terms of data on the right-hand side in divergence form. The relevant bound involves a Havin-Maz'ya- Wulff potential of the datum, and is a counterpart for…
We consider the 0-1 Incremental Knapsack Problem (IKP) where the capacity grows over time periods and if an item is placed in the knapsack in a certain period, it cannot be removed afterwards. The contribution of a packed item in each time…
The aim of the paper is to investigate on some questions of local regularity of a suitable weak solution to the Navier-Stokes Cauchy problem. The results are obtained in the wake of the ones, well known, by Caffarelli-Kohn-Nirenberg.
This work concerns the local convergence theory of Newton and quasi-Newton methods for convex-composite optimization: minimize f(x):=h(c(x)), where h is an infinite-valued proper convex function and c is C^2-smooth. We focus on the case…
We show that to every small and decaying solution of the linearized constraint equations about Minkowski spacetime, one can add a quadratically small correction to obtain a solution of the full constraint equations. Near spacelike infinity,…
We consider ultraweak variational formulations for (parametrized) linear first order transport equations in time and/or space. Computationally feasible pairs of optimally stable trial and test spaces are presented, starting with a suitable…
We show the local in time well-posedness of the Cauchy problem for the Kadomtsev-Petviashvili II equation for initial data in the non-isotropic Sobolev space H^{s_1,s_2}(R^2) with s_1 > -1/2 and s_2 \geq 0. On the H^{s_1,0}(R^2) scale this…
The KP-I equation arises as a weakly nonlinear model equation for gravity-capillary waves with Bond number $\beta>1/3$, also called strong surface tension. This equation has recently been shown to have a family of nondegenerate, symmetric…
In this paper we show the existence of weak solutions $w : M \rightarrow \mathbb{R}$ of the inverse mean curvature flow starting from a relatively compact set (possibly, a point) on a large class of manifolds satisfying Ricci lower bounds.…
The knapsack problem (KP) is a very famous NP-hard problem in combinatorial optimization. Also its generalization to multiple dimensions named d-dimensional knapsack problem (d-KP) and to multiple knapsacks named multiple knapsack problem…
A bilinear estimate in terms of Bourgain spaces associated with a linearised Kadomtsev-Petviashvili-type equation on the three-dimensional torus is shown. As a consequence, time localized linear and bilinear space time estimates for this…
We consider the Vlasov--Poisson system both in the repulsive (electrostatic potential) and in the attractive (gravitational potential) cases. In our first main theorem, we prove the uniqueness and the quantitative stability of Lagrangian…
We establish the higher differentiability of solutions to a class of obstacle problems for integral functionals where the convex integrand f satisfies p-growth conditions with respect to the gradient variable. We derive that the higher…
In this article we extend to generic $p$-energy minimizing maps between Riemannian manifolds a regularity result which is known to hold in the case $p=2$. We first show that the set of singular points of such a map can be quantitatively…
We construct and parametrize solutions to the constraint equations of general relativity in a neighborhood of Minkowski spacetime with arbitrary prescribed decay properties at infinity. We thus provide a large class of initial data for the…
We focus on the initial boundary value problem for a general scalar balance law in one space dimension. Under rather general assumptions on the flux and source functions, we prove the well-posedness of this problem and the stability of its…
We prove that the Cauchy problem of the mass-critical generalized KdV equation is globally well-posed in Sobolev spaces $H^s(\R)$ for $s>6/13$. Of course, we require that the mass is strictly less than that of the ground state in the…
We consider the initial value problem associated to a system consisting modified Korteweg-de Vries type equations $$ \partial_tv + \partial_x^3v + \partial_x(vw^2) =0,\ \ v(x,0)=\phi(x), $$ $$ \partial_tw + \alpha\partial_x^3w +…
Regularization plays a pivotal role when facing the challenge of solving ill-posed inverse problems, where the number of observations is smaller than the ambient dimension of the object to be estimated. A line of recent work has studied…