The limit of a nonlocal <i>p</i>-Laplacian obstacle problem with nonhomogeneous term as <i>p</i>→ ∞
<p dir="ltr">The aim of this paper is to investigate the asymptotic behavior of the minimizers to the following problems related to the fractional p-Laplacian with nonhomogeneous term ℎ(,) in the presence of an obstacle ψ in a bounded Lipschitz domain Ω⊂ℝ ,min{12∫Ω×Ω|()−()||−|+...
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2025
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| Summary: | <p dir="ltr">The aim of this paper is to investigate the asymptotic behavior of the minimizers to the following problems related to the fractional p-Laplacian with nonhomogeneous term ℎ(,) in the presence of an obstacle ψ in a bounded Lipschitz domain Ω⊂ℝ ,min{12∫Ω×Ω|()−()||−|+∫Ωℎ(,):∈,(Ω),≥ on ¯Ω,= on ∂Ω}.</p><p dir="ltr">In the case when ℎ(,)=ℎ(,) and ℎ(,)≥0 , we show the convergence of the solutions to certain limit as →∞ and identify the limit equation. More precisely, we show that the limit problem is closely related to the infinity fractional Laplacian. In the particular case when ∂ℎ>0 , we study the Hölder regularity of any solution to the limit problem and we extend the existence result to the case when h is not smooth. In addition, we will study the limit of this problem when the nonhomogeneous term ℎ(,) is not necessarily positive. To be more precise, we will consider the following two cases: ℎ(,)=ℎ() and ℎ(,)=ℎ()|| with Λ:=Λ()< .</p><h2 dir="ltr">Other Information</h2><p dir="ltr">Published in: Forum Mathematicum<br>License: <a href="http://creativecommons.org/licenses/by/4.0" target="_blank">http://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1515/forum-2025-0085" target="_blank">https://dx.doi.org/10.1515/forum-2025-0085</a></p> |
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