Global gradient estimates for non-uniformly elliptic equations

Byun, Sun‐Sig; Oh, Jehan

doi:10.1007/s00526-017-1148-2

Cited by 75 publications

(40 citation statements)

References 36 publications

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“…Is is interesting that despite that (D) does not possess the Lavrentiev phenomenon, still under the assumption that p and q are close enough, new regularity and a priori estimates appear. This is consistent with the results related to more general operators, see for instance [5] or [9,10,11]. Moreover, remark that under our assumptions, 2 ≤ τ ≤ s whereas 2 ≤ s ≤ ρ, and ρ = τ = s if p = q.…”

Section: Introductionsupporting

confidence: 91%

On the fractional regularity for degenerate equations with (p,q)-growth

Miranda

Presoto

2020

Nonlinear Analysis

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This paper addresses the gain of global fractional regularity in Nikolskii spaces for solutions of a class of quasilinear degenerate equations with (p, q)-growth. Indeed, we investigate the effects of the datum on the derivatives of order greater than one of the solutions of the (p, q)-Laplacian operator, under Dirichlet's boundary conditions. As it turns out, even in the absence of the socalled Lavrentiev phenomenon and without variations on the order of ellipticity of the equations, the fractional regularity of these solutions ramifies depending on the interplay between the growth parameters p, q and the data. Indeed, we are going to exploit the absence of this phenomenon in order to prove the validity up to the boundary of some regularity results, which are known to hold locally, and as well provide new fractional regularity for the associated solutions. In turn, there are obtained certain global regularity results by means of the combination between new a priori estimates and approximations of the differential operators, whereas the nonstandard boundary terms are handled by means of a careful choice for the local frame.2010 Mathematics Subject Classification. Primary: 35B45, 35B65, 35J70.

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Section: Introductionsupporting

confidence: 91%

On the fractional regularity for degenerate equations with (p,q)-growth

Miranda

Presoto

2020

Nonlinear Analysis

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“…have been recently studied, see for instance [7,9,31,55,56,57]. We stress that all of these special cases are covered by the results in this paper (cf.…”

Section: Introductionmentioning

confidence: 76%

Hölder continuity of $\omega$-minimizers of functionals with generalized Orlicz growth

Harjulehto¹,

Hästö²,

Lee³

2021

Annali Scuola Normale Superiore - Classe Di Scienze

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“…This has been left open in several papers on non-autonomous functionals [9,12,16,25,48]. Borderline cases are hard to catch.…”

Section: Introduction and Resultsmentioning

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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Global gradient estimates for non-uniformly elliptic equations

Cited by 75 publications

References 36 publications

On the fractional regularity for degenerate equations with (p,q)-growth

On the fractional regularity for degenerate equations with (p,q)-growth

Hölder continuity of $\omega$-minimizers of functionals with generalized Orlicz growth

Regularity for general functionals with double phase

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