3,190 research outputs found

    A symmetrization result for a class of anisotropic elliptic problems

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    We prove estimates for weak solutions to a class of Dirichlet problems associated to anisotropic elliptic equations with a zero order term.Comment: arXiv admin note: text overlap with arXiv:1607.0721

    Bizonytalanság vagy stabilitás?

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    Sántha Kálmán megjelent kötete a pedagógiai tartalmú kvalitatív kutatásmódszertannal foglalkozik. A szerző publikációinak egyik vonulatában, a már korábban megkezdett kutatásmódszertani paradigmák körüli dilemmák okainak feltárása terén szakmai törekvéseit tovább mélyíti. Az abdukció jelenségét mutatja be igen árnyaltan mint a valóság megismerésének és magyarázatának egyik eszközét

    Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle

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    In this paper we study optimal lower and upper bounds for functionals involving the first Dirichlet eigenvalue λF(p,Ω)\lambda_{F}(p,\Omega) of the anisotropic pp-Laplacian, 1<p<+1<p<+\infty. Our aim is to enhance how, by means of the P\mathcal P-function method, it is possible to get several sharp estimates for λF(p,Ω)\lambda_{F}(p,\Omega) in terms of several geometric quantities associated to the domain. The P\mathcal P-function method is based on a maximum principle for a suitable function involving the eigenfunction and its gradient

    A Bayesian numerical homogenization method for elliptic multiscale inverse problems

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    A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly oscillatory tensor from measurements of the fine scale solution at the boundary, using a coarse model based on numerical homogenization and model order reduction. We provide a rigorous Bayesian formulation of the problem, taking into account different possibilities for the choice of the prior measure. We prove well-posedness of the effective posterior measure and, by means of G-convergence, we establish a link between the effective posterior and the fine scale model. Several numerical experiments illustrate the efficiency of the proposed scheme and confirm the theoretical findings
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