Výsledky vyhledávání - "Borowski, Michał P."

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Discarding Lavrentiev's Gap in Non-automonous and Non-Convex Variational Problems

Autor: Borowski, Michał, Bousquet, Pierre, Chlebicka, Iwona, Lledos, Benjamin, Miasojedow, Błażej

We establish that the Lavrentiev gap between Sobolev and Lipschitz maps does not occur for a scalar variational problem of the form: \[ \textrm{to minimize} \qquad u \mapsto \int_\Omega f(x,u,\nabla u)\text{d}x \,, \] under a Dirichlet boundary condi

Externí odkaz: http://arxiv.org/abs/2410.14995

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Absence and presence of Lavrentiev's phenomenon for double phase functionals upon every choice of exponents

Autor: Borowski, Michał, Chlebicka, Iwona, De Filippis, Filomena, Miasojedow, Błażej

We study classes of weights ensuring the absence and presence of the Lavrentiev's phenomenon for double phase functionals upon every choice of exponents. We introduce a new sharp scale for weights for which there is no Lavrentiev's phenomenon up to a

Externí odkaz: http://arxiv.org/abs/2303.05877

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Absence of Lavrentiev's gap for anisotropic functionals

Autor: Borowski, Michał, Chlebicka, Iwona, Miasojedow, Błażej

We establish the absence of the Lavrentiev gap between Sobolev and smooth maps for a non-autonomous variational problem of a general structure, where the integrand is assumed to be controlled by a function which is convex and anisotropic with respect

Externí odkaz: http://arxiv.org/abs/2210.15217

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Boundedness of Wolff-type potentials and applications to PDEs

Autor: Borowski, Michał, Chlebicka, Iwona, Miasojedow, Błażej

We provide a short proof of a sharp rearrangement estimate for a generalized version of a potential of Wolff--Havin--Maz'ya type. As a consequence, we prove a reduction principle for that integral operators, that is, a characterization of those rearr

Externí odkaz: http://arxiv.org/abs/2209.05618

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Controlling monotonicity of nonlinear operators

Autor: Borowski, Michał, Chlebicka, Iwona

Controlling the monotonicity and growth of Leray--Lions' operators including the $p$-Laplacian plays a fundamental role in the theory of existence and regularity of solutions to second order nonlinear PDE. We collect, correct, and supply known estima

Externí odkaz: http://arxiv.org/abs/2110.14725

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