A C2-estimate for solutions of complex Monge-Ampère equations.
A comparison theorem for the Levi equation
We prove a strong comparison principle for the solution of the Levi equation , applying Bony Propagation Principle.
A general investigation of admissible couplings between systems of higher order and different type
A Liouville theorem for nonlinear elliptic systems with isotropic nonlinearities
A Note on the Problem -...u = ...u + u| u|2*-2.
A priori convergence of the greedy algorithm for the parametrized reduced basis method
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the a priori convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we...
A priori convergence of the Greedy algorithm for the parametrized reduced basis method
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the a priori convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we...
A priori convergence of the Greedy algorithm for the parametrized reduced basis method
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the a priori convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we...
Almost-Everywhere Regularity Results for Solutions of Non Linear Elliptic Systems.
An Age and Spatially Structured Population Model for Proteus Mirabilis Swarm-Colony Development
Proteus mirabilis are bacteria that make strikingly regular spatial-temporal patterns on agar surfaces. In this paper we investigate a mathematical model that has been shown to display these structures when solved numerically. The model consists of an ordinary differential equation coupled with a partial differential equation involving a first-order hyperbolic aging term together with nonlinear degenerate diffusion. The system is shown to admit global weak solutions.
An existence result for nonlinear evolution equations of second order
In this paper we consider a second order differential equation involving the difference of two monotone operators. Using an auxiliary equation, a priori bounds and a compactness argument we show that the differential equation has a local solution. An example is also presented in detail.
An existence theorem for the v. Kármán equations under the condition of free boundary
Application of Moser's method to a certain type of evolution equations
Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions [Book]
Arithmetic differential equations in several variables
We survey recent work on arithmetic analogues of ordinary and partial differential equations.