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Displaying 201 –
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1318
We give a unified statement and proof of a class of well known mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on the normal derivative at the boundary. These inequalities give rise to an energy quantization principle for sequences of solutions of boundary
value problems that have bounded energy and whose energy densities satisfy nonlinear bounds on the Laplacian and normal...
We consider the problem of electrical impedance tomography where conductivity distribution in a domain is to be reconstructed from boundary measurements of voltage and currents. It is well-known that this problem is highly illposed. In this work, we propose the use of the Mumford–Shah functional, developed for segmentation and denoising of images, as a regularization. After establishing existence properties of the resulting variational problem, we proceed by demonstrating the approach in several...
We consider the problem of electrical impedance tomography where conductivity
distribution in a domain is to be reconstructed from boundary measurements of
voltage and currents. It is well-known that this problem is highly
illposed. In this work, we propose the use of the Mumford–Shah functional,
developed for segmentation and denoising of images, as a regularization.
After establishing existence properties of the resulting variational problem,
we proceed by demonstrating the approach in several...
This work concerns an enlarged analysis of the problem of asymptotic compensation for a
class of discrete linear distributed systems. We study the possibility of asymptotic
compensation of a disturbance by bringing asymptotically the observation in a given
tolerance zone 𝒞. Under convenient hypothesis, we show the existence and the
unicity of the optimal control ensuring this compensation and we give its
characterization
Les méthodes sans maillage emploient une interpolation associée à un ensemble de particules : aucune information concernant la connectivité ne doit être fournie. Un des atouts de ces méthodes est que la discrétisation peut être enrichie d’une façon très simple, soit en augmentant le nombre de particules (analogue à la stratégie de raffinement ), soit en augmentant l’ordre de consistance (analogue à la stratégie de raffinement ). Néanmoins, le coût du calcul des fonctions d’interpolation est très...
Les méthodes sans maillage emploient une interpolation associée à un
ensemble de particules : aucune information concernant la connectivité ne doit être fournie.
Un des atouts de ces méthodes est que la discrétisation
peut être enrichie d'une
façon très simple, soit en augmentant le nombre de particules (analogue à la
stratégie de raffinement h), soit en augmentant l'ordre de consistance (analogue
à la stratégie de raffinement p). Néanmoins, le coût du calcul des fonctions
d'interpolation est...
We consider a class of semilinear elliptic equations of the formwhere , is a periodic, positive function and is modeled on the classical two well Ginzburg-Landau potential . We look for solutions to (1) which verify the asymptotic conditions as uniformly with respect to . We show via variational methods that if is sufficiently small and is not constant, then (1) admits infinitely many of such solutions, distinct up to translations, which do not exhibit one dimensional symmetries.
We consider a class of
semilinear elliptic equations of the form
15.7cm
-
where , is a periodic, positive function and
is modeled on the classical two well Ginzburg-Landau
potential . We look for solutions to ([see full textsee full text])
which verify the
asymptotic conditions as
uniformly with respect to .
We show via variational
methods that if ε is sufficiently small and a is not constant,
then ([see full textsee full text])
admits infinitely many of such solutions, distinct...
We study nonlinear elliptic equations of the form where the main assumption on and is that there exists a one dimensional solution which solves the equation in all the directions . We show that entire monotone solutions are one dimensional if their level set is assumed to be Lipschitz, flat or bounded from one side by a hyperplane.
Currently displaying 201 –
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1318