Weak solutions to general Euler's equations via nonsmooth critical point theory
Weak solutions to the complex Hessian equation
We investigate the class of functions associated with the complex Hessian equation .
Weak uniqueness and partial regularity for the composite membrane problem
We study the composite membrane problem in all dimensions. We prove that the minimizing solutions exhibit a weak uniqueness property which under certain conditions can be turned into a full uniqueness result. Next we study the partial regularity of the solutions to the Euler–Lagrange equation associated to the composite problem and also the regularity of the free boundary for solutions to the Euler–Lagrange equations.
Weak-element Approximations to Elliptic Differential Equations.
Weakly sequentially continuous maps and existence principles for elliptic equations
We present a Furi-Pera type theorem for weakly sequentially continuous maps. As an application we establish new existence principles for elliptic Dirichlet problems.
Weak-Type (1-1) Inequality for the Monge-Ampère SIO's.
Wegner estimates and Anderson localization for alloy-type potentials.
Weighted Dispersive Estimates for Solutions of the Schrödinger Equation
2000 Mathematics Subject Classification: 35L15, 35B40, 47F05.Introduction and statement of results. In the present paper we will be interested in studying the decay properties of the Schrödinger group.The authors have been supported by the agreement Brazil-France in Mathematics – Proc. 69.0014/01-5. The first two authors have also been partially supported by the CNPq-Brazil.
Weighted inequalities for gradients on non-smooth domains [Book]
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...
Weighted Sobolev and Poincaré Inequalities and Quasiregular Mappings of Polynomial Type.
Well-posedness of the difference schemes of the high order of accuracy for elliptic equations.
Well-posedness of the Dirichlet problem and homotopy classification of elliptic systems of second-order partial differential equations
Wesentliche Selbstadjungiertheit eines Schrödinger-Operators.
What is the smallest possible constant in Céa's lemma?
We consider finite element approximations of a second order elliptic problem on a bounded polytopic domain in with . The constant appearing in Céa’s lemma and coming from its standard proof can be very large when the coefficients of an elliptic operator attain considerably different values. We restrict ourselves to regular families of uniform partitions and linear simplicial elements. Using a lower bound of the interpolation error and the supercloseness between the finite element solution and...
When is the first eigenfunction for the clamped plate equation of fixed sign?
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...
Which solutions of the third problem for the Poisson equation are bounded?