On -estimates for the time dependent Schrödinger operator on .
On Liouville theorem and apriori estimates for the scalar curvature equations
On Lyapunov-type inequalities for two-dimensional nonlinear partial systems.
On minima of variational problems with some nonconvex constraints.
On multiquasielliptic equations in .
On periodic solutions of a special type of the beam equation
The paper deals with the existence of time-periodic solutions to the beam equation, in which terms expressing torsion and damping are also considered. The existence of periodic solutions is proved in the cas of time-periodic outer forces by means of an apriori estimate and the Fourier method.
On positive Rockland operators
Let G be a homogeneous Lie group with a left Haar measure dg and L the action of G as left translations on . Further, let H = dL(C) denote a homogeneous operator associated with L. If H is positive and hypoelliptic on we prove that it is closed on each of the -spaces, p ∈ 〈 1,∞〉, and that it generates a semigroup S with a smooth kernel K which, with its derivatives, satisfies Gaussian bounds. The semigroup is holomorphic in the open right half-plane on all the -spaces, p ∈ [1,∞]. Further extensions...
On positive solutions of semilinear elliptic problems
On quasilinear elliptic equations in domains with conical boundary points.
On Quasilinear Elliptic Systems of Diagonal Form.
On solvability of boundary value problem for elliptic equations with Bitsadze-Samarskij condition.
On some improperly posed problem for a degenerate nonlinear parabolic equation.
On some -estimates for solutions of elliptic equations in unbounded domains
In this review article we present an overview on some a priori estimates in , , recently obtained in the framework of the study of a certain kind of Dirichlet problem in unbounded domains. More precisely, we consider a linear uniformly elliptic second order differential operator in divergence form with bounded leading coeffcients and with lower order terms coefficients belonging to certain Morrey type spaces. Under suitable assumptions on the data, we first show two -bounds, , for the solution...
On some nonlinear elliptic systems with coercive perturbation in RN.
A nonlinear elliptic system involving the p-Laplacian is considered in the whole RN. Existence of nontrivial solutions is obtained by applying critical point theory; also a regularity result is established.
On Squeezing and Flow of Energy for Nonlinear Wave Equations.
On the boundedness of the mapping in Besov spaces
For , precise conditions on the parameters are given under which the particular superposition operator is a bounded map in the Besov space . The proofs rely on linear spline approximation theory.
On the Charney Conjecture of Data Assimilation Employing Temperature Measurements Alone: The Paradigm of 3D Planetary Geostrophic Model
Analyzing the validity and success of a data assimilation algorithmwhen some state variable observations are not available is an important problem in meteorology and engineering. We present an improved data assimilation algorithm for recovering the exact full reference solution (i.e. the velocity and temperature) of the 3D Planetary Geostrophic model, at an exponential rate in time, by employing coarse spatial mesh observations of the temperature alone. This provides, in the case of this paradigm,...
On the Dirichlet problem for quasilinear elliptic second order equations with triple degeneracy and singularity in a domain with a boundary conical point.
On the Euler equations of incompressible perfect fluids
On the existence of a classical solution of a mixed boundary problem for a second order one-dimensional hyperbolic equation. II.