Weighted Miranda-Talenti inequality and applications to equations with discontinuous coefficients
Let be an open bounded set in , with boundary, and (, ) be a weighted Morrey space. In this note we prove a weighted version of the Miranda-Talenti...
Weighted Poincaré and Sobolev inequalites for vector fields satisfying Hörmander's condition and applications.
In this paper we mainly prove weighted Poincaré inequalities for vector fields satisfying Hörmander's condition. A crucial part here is that we are able to get a pointwise estimate for any function over any metric ball controlled by a fractional integral of certain maximal function. The Sobolev type inequalities are also derived. As applications of these weighted inequalities, we will show the local regularity of weak solutions for certain classes of strongly degenerate differential operators formed...
Well posed Cauchy problems for complex nonlinear equations must be semilinear.
Well posedness under Levi conditions for a degenerate second order Cauchy problem
Well-posedness and regularity for a parabolic-hyperbolic Penrose-Fife phase field system
This work is concerned with the study of an initial boundary value problem for a non-conserved phase field system arising from the Penrose-Fife approach to the kinetics of phase transitions. The system couples a nonlinear parabolic equation for the absolute temperature with a nonlinear hyperbolic equation for the phase variable , which is characterized by the presence of an inertial term multiplied by a small positive coefficient . This feature is the main consequence of supposing that the response...
Well-posedness and regularity results for a dynamic von Kármán plate.
Wellposedness and stability results for the Navier-Stokes equations in
Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations
Well-posedness for systems representing electromagnetic/acoustic wavefront interaction
In this paper we consider dispersive electromagnetic systems in dielectric materials in the presence of acoustic wavefronts. A theory for existence, uniqueness, and continuous dependence on data is presented for a general class of systems which include acoustic pressure-dependent Debye polarization models for dielectric materials.
Well-posedness for Systems Representing Electromagnetic/Acoustic Wavefront Interaction
In this paper we consider dispersive electromagnetic systems in dielectric materials in the presence of acoustic wavefronts. A theory for existence, uniqueness, and continuous dependence on data is presented for a general class of systems which include acoustic pressure-dependent Debye polarization models for dielectric materials.
Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid
In this paper, we consider the interaction between a rigid body and an incompressible, homogeneous, viscous fluid. This fluid-solid system is assumed to fill the whole space , or . The equations for the fluid are the classical Navier-Stokes equations whereas the motion of the rigid body is governed by the standard conservation laws of linear and angular momentum. The time variation of the fluid domain (due to the motion of the rigid body) is not known a priori, so we deal with a free boundary...
Well-posedness in the Gevrey classes of the Cauchy problem for a non-strictly hyperbolic equation with coefficients depending on time
Well-posedness of the Cauchy problem for hyperbolic equations with non-Lipschitz coefficients.
Well-posedness of the Dirichlet problem and homotopy classification of elliptic systems of second-order partial differential equations
Well-posedness results for a model of damage in thermoviscoelastic materials
When does the free boundary enter into corner points of the fixed boundary?
When is the first eigenfunction for the clamped plate equation of fixed sign?
Which electric fields are realizable in conducting materials?
In this paper we study the realizability of a given smooth periodic gradient field ∇u defined in Rd, in the sense of finding when one can obtain a matrix conductivity σ such that σ∇u is a divergence free current field. The construction is shown to be always possible locally in Rd provided that ∇u is non-vanishing. This condition is also necessary in dimension two but not in dimension three. In fact the realizability may fail for non-regular gradient fields, and in general the conductivity cannot...
Which sequences of holes are admissible for periodic homogenization with Neumann boundary condition?
In this paper we give a general presentation of the homogenization of Neumann type problems in periodically perforated domains, including the case where the shape of the reference hole varies with the size of the period (in the spirit of the construction of self-similar fractals). We shows that -convergence holds under the extra assumption that there exists a bounded sequence of extension operators for the reference holes. The general class of Jones-domains gives an example where this result applies....
Which sequences of holes are admissible for periodic homogenization with Neumann boundary condition?
In this paper we give a general presentation of the homogenization of Neumann type problems in periodically perforated domains, including the case where the shape of the reference hole varies with the size of the period (in the spirit of the construction of self-similar fractals). We shows that H0-convergence holds under the extra assumption that there exists a bounded sequence of extension operators for the reference holes. The general class of Jones-domains gives an example where this result...