Advances in remote sensing technology are now providing tools to support geospatial mapping of the soil properties for the application to the management of agriculture and the environment. In this paper results of visible and near IR spectral reflectance are presented and discussed. A supportable evaluation of organic matter in the soil is the absence of a specific signature, this concept arose out of the widely shared observation of scientific community in this concern. The obtained results show that a morphologic approach based on an experimental distance model is an appropriate and efficient method to deal with this matter

In this paper we illustrate the lineguides of our research group. We describe some recent results concerning the study of some nonlinear differential equations and systems having a variational nature and arising from physics, geometry and applied sciences. In particular we report existence, multiplicity and regularity results for the solutions of these nonlinear problems. We point out that, in treating the above problems, the used methods for finding solutions are variational and topological, indeed the existence of solutions of the considered equations is obtained searching for critical points of suitable functionals defined on manifolds embedded into infinite dimensional functional spaces, while the regularity of the solutions is studied by means of geometric and harmonic analysis tools.

This papers deals with PI and PID control of second order systems with an input hysteresis described by a modified Prandtl-Ishlinskii model. The problem of the asymptotic tracking of constant references is re-formulated as the stability of a polytopic linear differential inclusion. This offers a simple linear matrix inequality condition that, when satisfied with the chosen PI or PID controller gains, ensures the tracking of constant reference and also allows the design to establish a performance index. The validation of the approach is performed experimentally on a Magnetic Shape Memory Alloy micrometric positioning system

We derive global gradient estimates in Morrey spaces for the weak solutions to discontinuous quasilinear elliptic equations related to important variational problems arising in models of linearly elastic laminates and composite materials. The principal coefficients of the quasilinear operator are supposed to be merely measurable in one variable and to have small-BMO seminorms in the remaining orthogonal directions, and the nonlinear terms are subject to controlled growth conditions with respect to the unknown function and its gradient. The boundary of the domain considered is Reifenberg flat which includes boundaries with rough fractal structure. As outgrowth of the main result we get global Hoelder continuity of the weak solution with exact value of the corresponding exponent.

We prove global essential boundedness of weak solutions to quasilinear coercive divergence form equations with data belonging to Morrey spaces. The nonlinear terms are given in terms of Carath'eodory functions and satisfy controlled growth assumptions. As an application of the main result, we get global H"older continuity of the solutions to semilinear elliptic equations with measurable coefficients and Morrey data."

We establish a global weighted $W^{1,p}$-regularity for solutions to variational inequalities and obstacle problems for divergence form elliptic systems with measurable coefficients in bounded non-smooth domains.

The note deals with solutions to the Dirichlet problem for general quasilinear divergence-form elliptic operators whose prototype is the p-Laplacean operator. The nonlinear terms are given by Carathéodory functions and satisfy the natural structure conditions of Ladyzhenskaya and Ural’tseva with data belonging to suitable Morrey spaces. The fairly non-regular boundary of the underlying domain is supposed to satisfy a capacity density condition which allows domains with exterior cone (or even corkscrew) property. We prove Hölder continuity up to the boundary for the boundedweak solutions of such equations, generalizing thisway the classical L^p -result of Ladyzhenskaya and Ural’tseva to the settings of the Morrey spaces.

We consider a parabolic system in divergence form with measurable coefficients in a nonsmooth bounded domain to obtain a global gradient estimate for the weak solution in the setting of Orlicz space which is a natural generalization of Lp space. The coefficients are assumed to be merely measurable in one spatial variable and have small bounded mean oscillation semi-norms in all the other variables. The boundary of the domain can be locally approximated by a hyperplane, a so-called δ-Reifenberg domain which is beyond the Lipschitz category.

The results by Palagachev (2009) [3] regarding global Holder continuity for the weak solutions to quasilinear divergence form elliptic equations are generalized to the case of nonlinear terms with optimal growths with respect to the unknown function and its gradient. Moreover, the principal coefficients are discontinuous with discontinuity measured in terms of small BMO norms and the underlying domain is supposed to have fractal boundary satisfying a condition of Reifenberg flatness. The results are extended to the case of parabolic operators as well.

We obtain global essential boundedness and H"older continuity of the weak solutions to quasilinear elliptic equations in divergence form with data lying in Morrey spaces."

We derive weak solvability and higher integrability of the spatial gradient of solutions to Cauchy-Dirichlet problem for divergence form quasi-linear parabolic equations {u(t) - div (a(ij)(x, t, u)D(j)u + a(i)(x, t, u)) = b(x, t, u, Du) in Q, u = 0 on partial derivative(p)Q, where Q is a cylinder in R(n) x (0, T) with Reifenberg flat base Omega. The principal coefficients a(ij)(x, t, u) of the uniformly parabolic operator are supposed to have small BMO norms with respect to (x, t) while the nonlinear terms a(i)(x, t, u) and b(x, t, u, Du) support controlled growth conditions.

We are concerned with optimal regularity theory in weighted Sobolev spaces for discontinuous nonlinear parabolic problems in divergence form over a non-smooth bounded domain. Assuming smallness in BMO of the principal part of the nonlinear operator and flatness in Reifenberg sense of the boundary we establish a global weighted $W^{1,p}$ estimate for the weak solutions of such problems by proving that the spatial gradient and the nonhomogeneous term belong to the same weighted Lebesgue space. The result is new in the settings of nonlinear parabolic problems.

We obtain a global weighted $L^p$ estimate for the gradient of the weak solutions to divergence form elliptic equations with measurable coefficients in a nonsmooth bounded domain. The coefficients are assumed to be merely measurable in one variable and to have small BMO semi-norms in the remaining variables, while the boundary of the domain is supposed to be Reifenberg flat, which goes beyond the category of domains with Lipschitz continuous boundaries. As consequence of the main result, we derive global gradient estimate for the weak solution in the framework of the Morrey spaces which implies global H"older continuity of the solution."