The Cauchy–Dirichlet problem for a general class of parabolic equations

Baroni, Paolo; Lindfors, Casimir

doi:10.1016/j.anihpc.2016.03.003

Cited by 36 publications

(37 citation statements)

References 29 publications

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“…holds for every s > 0 (see [8] for more details). We shall later use the following Young type inequality, valid for every ε ∈ (0, 1) and s, t ≥ 0:…”

Section: Notation and Preliminariesmentioning

confidence: 99%

Regularity for general functionals with double phase

2018

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We prove sharp regularity results for a general class of functionals of the typefeaturing non-standard growth conditions and non-uniform ellipticity properties. The model case is given by the double phase integralThis changes its ellipticity rate according to the geometry of the level set {a(x) = 0} of the modulating coefficient a(·). We also present new methods and proofs, that are suitable to build regularity theorems for larger classes of non-autonomous functionals. Finally, we disclose some new interpolation type effects that, as we conjecture, should draw a general phenomenon in the setting of non-uniformly elliptic problems. Such effects naturally connect with the Lavrentiev phenomenon.

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“…holds for every s > 0 (see [8] for more details). We shall later use the following Young type inequality, valid for every ε ∈ (0, 1) and s, t ≥ 0:…”

Section: Notation and Preliminariesmentioning

confidence: 99%

Regularity for general functionals with double phase

2018

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“…≤ H 0 (t), see [5] for more details. Now, using (4.20) 1 , (4.12), (4.18), (4.24) and (4.21) we estimate, for a certain fixed σ ∈ (0, 1),…”

Section: Corollary 3 Let U ∈ W 1h(·)mentioning

confidence: 99%

Regularity for multi-phase variational problems

Filippis

2019

Journal of Differential Equations

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“…However, the step proving local boundedness of the gradients was still missing. For equations this gap was closed independently by Baroni and Lindfors [3,Theorem 1.2]. In this work we prove the boundedness of the gradients in to the general vectorial case.…”

Section: Introductionmentioning

confidence: 66%

Regularity for parabolic systems of Uhlenbeck type with Orlicz growth

Diening

Scharle

Schwarzacher

2019

Journal of Mathematical Analysis and Applications

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We study the local regularity of p-caloric functions or more generally of ϕ-caloric functions. In particular, we study local solutions of non-linear parabolic systems with homogeneous right hand side, where the leading terms has Uhlenbeck structure of Orlicz type. This paper closes the gap of [22] where Liebermann proved that if the gradient of a solution is bounded, it is Hölder continuous.The crucial step is a novel local estimates for the gradient of the solutions, which generalize and improve the pioneering estimates of DiBenedetto and Friedman [12,10] for the p-Laplace heat equation.

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The Cauchy–Dirichlet problem for a general class of parabolic equations

Cited by 36 publications

References 29 publications

Regularity for general functionals with double phase

Regularity for general functionals with double phase

Regularity for multi-phase variational problems

Regularity for parabolic systems of Uhlenbeck type with Orlicz growth

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