Existence and local boundedness of solutions of a -Laplacian problem

Arriagada, Waldo; Huentutripay, Jorge

doi:10.1080/00036811.2017.1404581

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…For Ω = R N , Φ = Ψ, N > P Φ , and g ∈ L r (Ω) ∩ L ∞ (Ω) where r = r(Φ) > 0, see [9,10]. For bounded Ω and Ψ ≺≺ Φ * (Φ * is the Sobolev conjugate [1, Page 248]), see [31, g ≡ 1], and for g ∈ L Ã(Ω), where A = Φ * • Φ −1 , see [46].…”

Section: Introductionmentioning

confidence: 99%

Admissible function spaces for weighted Sobolev inequalities

Anoop¹,

Biswas²,

Das³

2021

CPAA

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Let , ∈ N with 1 ≤ ≤ and let Ω = Ω 1 × Ω 2 be an open set in R × R − . For ∈ (1, ∞) and ∈ (0, ∞), we consider the following weighted Sobolev type inequality:for some > 0. Depending on the values of , , , we have identified various pairs of Lorentz spaces, Lorentz-Zygmund spaces and weighted Lebesgue spaces for ( 1 , 2 ) so that (0.1) holds. Furthermore, we give a sufficient condition on 1 , 2 so that the best constant in (0.1) is attained in the Beppo-Levi space 1, 0 (Ω)-the completion of 1 (Ω) with respect to ‖∇ ‖ (Ω) .

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Section: Introductionmentioning

confidence: 99%

Admissible function spaces for weighted Sobolev inequalities

Anoop¹,

Biswas²,

Das³

2021

CPAA

View full text Add to dashboard Cite

show abstract

“…The existence of nontrivial solutions of equations in the divergence form is proved in [5]via a classical Lagrange rule. This result is somewhat motivated by the ideas in [14,Theorem 3.1].…”

Section: Introductionmentioning

confidence: 99%

“…The proof of [21,Theorem 2.2] follows similar lines but in a different, nonhomogeneous context. The local boundedness of nontrivial solutions has been addressed in [5] as well. Our results are closely related to the study of the asymptotic properties of particular subsequences of eigenvalues.…”

Section: Introductionmentioning

confidence: 99%