Improved integrability and boundedness of solutions to some high-order variational problems

Voitovych, Mykhailo V.

doi:10.1007/s10958-018-4061-0

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Preliminaries and Statement Of The Results1

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2022

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Cited by 5 publications

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“…We point out that the assumption (2.4) on f required in Theorems 2.2 and 2.3 is the same which yields to the existence of bounded and Hölder continuous solutions for nondegenerate (i.e., θ = 0) fourth-order equations. In this last case, examples of unbounded solutions of equation (1.1), with f ∈ L N q (Ω) and f / ∈ L N q +ε (Ω), for any ε > 0, are constructed in [48].…”

Section: Preliminaries and Statement Of The Resultsmentioning

confidence: 99%

Existence of Hölder Continuous Solutions for a Class of Degenerate Fourth-Order Elliptic Equations

Cirmi¹,

D’Asero²,

Leonardi³

2022

Mediterr. J. Math.

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Section: Preliminaries and Statement Of The Resultsmentioning

confidence: 99%

Existence of Hölder Continuous Solutions for a Class of Degenerate Fourth-Order Elliptic Equations

Cirmi¹,

D’Asero²,

Leonardi³

2022

Mediterr. J. Math.

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$$ {\mathfrak{B}}_1 $$ classes of De Giorgi, Ladyzhenskaya, and Ural’tseva and their application to elliptic and parabolic equations with nonstandard growth

Skrypnik

Voitovych

2020

J Math Sci

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We introduce elliptic and parabolic B 1 classes that generalize the well-known B p classes of De Giorgi, Ladyzhenskaya and Ural'tseva with p > 1. New classes are applied to prove pointwise continuity of solutions of elliptic and parabolic equations with nonstandard growth conditions. Our considerations cover new cases of variable exponent and (p, q)-phase growth including the ,,singular-degenerate" parabolic case p < 2 < q.

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On the generalized Um,pf classes of De Giorgi-Ladyzhenskaya-Ural'tseva and pointwise estimates of solutions to high-order elliptic equations via Wolff potentials

Skrypnik

Voitovych

2020

Journal of Differential Equations

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Improved integrability and boundedness of solutions to some high-order variational problems

Cited by 5 publications

References 11 publications

Existence of Hölder Continuous Solutions for a Class of Degenerate Fourth-Order Elliptic Equations

Existence of Hölder Continuous Solutions for a Class of Degenerate Fourth-Order Elliptic Equations

$$ {\mathfrak{B}}_1 $$ classes of De Giorgi, Ladyzhenskaya, and Ural’tseva and their application to elliptic and parabolic equations with nonstandard growth

On the generalized Um,pf classes of De Giorgi-Ladyzhenskaya-Ural'tseva and pointwise estimates of solutions to high-order elliptic equations via Wolff potentials

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