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A Struwe-type Decomposition Result for Weighted Critical $p$-Laplace Equations

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arxiv 2410.14861 v1 pith:WVYTMKS2 submitted 2024-10-18 math.AP

Edward Chernysh This is my paper · ORCID
classification math.AP
keywords criticalequationslaplacestruwe-typeaccountboundedcaffarelli-kohn-nirenbergclass
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abstract

We establish Struwe-type decompositions of Palais-Smale sequences for a class of critical $p$-Laplace equations of the Caffarelli-Kohn-Nirenberg type in a bounded domain $\Omega\subset\mathbb{R}^n$, $n\ge2$, containing the origin. In doing so, we highlight important differences introduced by the weights and require new rescaling laws to account for this new framework.

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  1. Global Compactness Result for a Br\'ezis-Nirenberg-Type Problem Involving Mixed Local Nonlocal Operator

    math.AP 2025-04 conditional novelty 6.0 of 10

    A Palais-Smale sequence for the mixed local-nonlocal critical problem decomposes into a weak limit and classical Sobolev bubbles, yielding a Coron-type existence theorem for large dimensions.

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