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.
On the existence of a fundamental solution for a parabolic differential equation with unbounded coefficients
On the Fejér-F. Riesz inequality in
On the global well-posedness of the Boussinesq system with zero viscosity
In this paper we prove the global well-posedness of the two-dimensional Boussinesq system with zero viscosity for rough initial data.
On the Klainerman–Machedon conjecture for the quantum BBGKY hierarchy with self-interaction
We consider the 3D quantum BBGKY hierarchy which corresponds to the -particle Schrödinger equation. We assume the pair interaction is . For the interaction parameter , we prove that, provided an energy bound holds for solutions to the BBKGY hierarchy, the limit points satisfy the space-time bound conjectured by S. Klainerman and M. Machedon [45] in 2008. The energy bound was proven to hold for in [28]. This allows, in the case , for the application of the Klainerman–Machedon uniqueness theorem...
On the local behaviour of solutions of a certain class of doubly nonlinear parabolic equations.
On the long-time behaviour of solutions of the p-Laplacian parabolic system
Convergence of global solutions to stationary solutions for a class of degenerate parabolic systems related to the p-Laplacian operator is proved. A similar result is obtained for a variable exponent p. In the case of p constant, the convergence is proved to be , and in the variable exponent case, L² and -weak.
On the optimality of velocity averaging lemmas