A Cauchy problem for . Asymptotic behaviour of solutions
A class of pseudo differential operators with multiple non-involutive characteristics
A field equation defined by a Hurwitz pair
A general controllability theorem
A Geometric Intrepertation for the Hans Lewy Operator
A geometrical interpretation of the time evolution of the Schrödinger equation for discrete quantum systems
A note on the Dirichlet problem for the elliptic linear operator in Sobolev spaces with weight
A partial differential operator which is surjective on Gevrey classes with 1 ≤ d < 2 and d ≥ 6 but not for 2 ≤ d < 6
It is shown that the partial differential operator is surjective if 1 ≤ d < 2 or d ≥ 6 and not surjective for 2 ≤ d < 6.
A posteriori estimations of approximate solutions for some types of boundary value problems
A priori estimates for higher order hyperbolic equations.
A recursion operator for the universal hierarchy equation via Cartan’s method of equivalence
We apply Cartan’s method of equivalence to find a Bäcklund autotransformation for the tangent covering of the universal hierarchy equation. The transformation provides a recursion operator for symmetries of this equation.
A symmetrization result for elliptic equations with lower-order terms
A symmetrization result for nonlinear elliptic equations.
We consider a solution u of the homogeneous Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = g(x,u) + f, where the principal term is a Leray-Lions operator defined on W01,p (Ω). The function g(x,u) satisfies suitable growth assumptions, but no sign hypothesis on it is assumed. We prove that the rearrangement of u can be estimated by the solution of a problem whose data are radially symmetric.
A Two-Particle Quantum System with Zero-Range Interaction
We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators.
Algorithmic construction of hyperfunction solutions to invariant differential equations on the space of real symmetric matrices.
Almost product structures and Monge-Ampère equations.
An estimate of the gap of the first two eigenvalues in the Schrödinger operator
Analytic and Gevrey Hypoellipticity
Applications of symmetry methods to the theory of plasma physics.