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Cited by 8 publications
(10 citation statements)
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References 11 publications
(18 reference statements)
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“…Assumption (2.5), up to the addition of a whichever bounded vector filed, prescribes a threshold on the M N (Ω)-norm of E (see also [7] and [12]). As already said in the introduction, this smallness condition is sharp and cannot be weakened (see [17] and Remark 4.5). To clarify the different notation between (1.10) and (2.5), let us notice that…”
Section: Resultsmentioning
confidence: 85%
See 2 more Smart Citations
“…Assumption (2.5), up to the addition of a whichever bounded vector filed, prescribes a threshold on the M N (Ω)-norm of E (see also [7] and [12]). As already said in the introduction, this smallness condition is sharp and cannot be weakened (see [17] and Remark 4.5). To clarify the different notation between (1.10) and (2.5), let us notice that…”
Section: Resultsmentioning
confidence: 85%
“…In the borderline case γ(B) = N −2m N m estimates with logarithmic corrections are obtained. This argument shows that if (2.5) is not satisfied the standard relation between the regularity of the data and the solution is lost (for a more detailed description of this fact see [17]). Now we are in the position of proving Theorems 2.1 and 2.2.…”
Section: We Deduce By Direct Computation Of the Gradient Thatmentioning
confidence: 99%
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“…where 0 ∈ Ω, µ ∈ R + , A ∈ R. The inequality (1.10) where a(x) = µ u |x| 2 and E(x) = A x |x| 2 is satisfied by the real numbers R > 0 such that A 2 µ ≤ R. In [13], the existence of very singular distributional solutions u ∈ W 1,q 0 (Ω), for every q <…”
Section: Convection Equation Remark Consider the Boundary Value Problemmentioning
confidence: 99%
“…Furthermore, in the same paper, the existence of entropy solutions to problem (5) also be considered provided E ∈ ðL 2 ðΩÞÞ N and f ∈ L 1 ðΩÞ. Recently, continuation of [2], Boccardo and Orsina [3] studied the existence of distributional solution u ∈ W 1,q 0 ðΩÞ to problem (5) with q < Nα/A + α provided αðN − 2Þ ≤ A < αðN − 1Þ and f ∈ L 1 ðΩÞ. Moreover, u verifies a prior estimation:…”
Section: Introductionmentioning
confidence: 99%