The Kolmogorov equation with time-measurable coefficients.
The linear-quadratic optimal control problem for delay differential equations
In questo lavoro si considera il problema del controllo ottimo per un'equazione lineare con ritardo in uno spazio di Hilbert, con costo quadratico. Si dimostra che il problema della sintesi si traduce in una equazione di Riccati in uno opportuno spazio prodotto e si prova che tale equazione ammette un’unica soluzione.
The local ill-posedness of the modified KdV equation
The long-time behaviour of the solutions to semilinear stochastic partial differential equations on the whole space
The Cauchy problem for a stochastic partial differential equation with a spatial correlated Gaussian noise is considered. The "drift" is continuous, one-sided linearily bounded and of at most polynomial growth while the "diffusion" is globally Lipschitz continuous. In the paper statements on existence and uniqueness of solutions, their pathwise spatial growth and on their ultimate boundedness as well as on asymptotical exponential stability in mean square in a certain Hilbert space of weighted functions...
The -Wright function in time-fractional diffusion processes: a tutorial survey.
The mean curvature measure
We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is weakly continuous with respect to almost everywhere convergence. We also establish a sharp Harnack inequality for the minimal surface equation, which is crucial for our proof of the weak continuity. As an application we prove the existence of weak solutions to the...
The method of fictitious domains in the Signorini problem.
The method of lines for hyperbolic stochastic functional partial differential equations
We apply an approximation by means of the method of lines for hyperbolic stochastic functional partial differential equations driven by one-dimensional Brownian motion. We study the stability with respect to small -perturbations.
The Method of Lines for Poisson's Equation with Nonlinear or Free Boundary Conditions.
The micro-support of the complex defined by a convolution operator in tube domains
The mixed problem for an infinite system of first order functional differential equations.
The motion of the free surface of a liquid
The non-uniqueness of the limit solutions of the scalar Chern-Simons equations with signed measures
We investigate the effect of admitting signed measures as a datum at the scalar Chern-Simons equation with the Dirichlet boundary condition. Approximating by a sequence of functions or finite signed measures such that this equation has a solution for each , we are interested in establishing the convergence of the sequence to a function and describing the form of the measure which appears on the right-hand side of the scalar Chern-Simons equation solved by .
The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes
We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in time and decays with a quantitative rate to the trivial solution. The proof uses the robust vector field method. It makes use of the decay properties of the linear wave equation on Kerr spacetime, in particular the improved decay rates in the region .
The obstacle problem for the biharmonic operator
The output least squares identifiability of the diffusion coefficient from an H–observation in a 2–D elliptic equation
Output least squares stability for the diffusion coefficient in an elliptic equation in dimension two is analyzed. This guarantees Lipschitz stability of the solution of the least squares formulation with respect to perturbations in the data independently of their attainability. The analysis shows the influence of the flow direction on the parameter to be estimated. A scale analysis for multi-scale resolution of the unknown parameter is provided.
The Output Least Squares Identifiability of the Diffusion Coefficient from an H1–Observation in a 2–D Elliptic Equation
Output least squares stability for the diffusion coefficient in an elliptic equation in dimension two is analyzed. This guarantees Lipschitz stability of the solution of the least squares formulation with respect to perturbations in the data independently of their attainability. The analysis shows the influence of the flow direction on the parameter to be estimated. A scale analysis for multi-scale resolution of the unknown parameter is provided.
The -Laplacian – mascot of nonlinear analysis
The p-harmonic system with measure-valued right hand side
The phase field equations and gradient flows of marginal functions.