Loading [MathJax]/extensions/MathZoom.js
The theory of
compensated compactness of Murat and Tartar links the algebraic condition
of rank-r convexity with the analytic condition of weak
lower
semicontinuity. The former is an algebraic
condition and therefore it is, in principle, very easy to use. However,
in applications of this theory, the need for an efficient classification of
rank-r convex forms arises. In the present paper,
we define the concept of extremal 2-forms and characterize them
in the rotationally invariant jointly...
We provide an existence result for a system of quasilinear equations subject to nonlinear boundary conditions on a bounded domain by using the fibering method.
We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a replacement lemma which has as a corollary a maximum principle for minimizers.
We prove the existence of a sequence of radial solutions with negative energy of the Schrödinger-Maxwell equations under the action of a negative potential.
We study a nonlinear elliptic system with resonance part and nonlinear boundary conditions on an unbounded domain. Our approach is variational and is based on the well known Landesman-Laser type conditions.
We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic coercive partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced-basis approximations – Galerkin projection onto a space spanned by solutions of the governing partial differential equation at selected points in parameter space; (ii) a posteriori error estimation – relaxations of the error-residual equation...
We present a technique for the rapid and reliable prediction of
linear-functional
outputs of elliptic coercive partial differential equations with affine
parameter dependence. The essential components are (i )
(provably) rapidly
convergent global reduced-basis approximations – Galerkin projection
onto a space
WN spanned by solutions of the governing partial differential
equation at N
selected points in parameter space; (ii ) a posteriori
error estimation
– relaxations of the error-residual equation...
In this paper we prove a regularity
result for local minimizers of functionals of the Calculus of Variations of the
typewhere Ω is a bounded open set in , u∈(Ω; ), p> 1, n≥ 2 and N≥ 1.
We use the technique of difference quotient without the usual assumption on the growth of the second derivatives of the function f. We apply this result to give
a bound on the Hausdorff dimension of the singular set of minimizers.
Currently displaying 1 –
20 of
165