| Naslov: | Trilinear embedding for divergence-form operators with complex coefficients |
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| Avtorji: | ID Carbonaro, Andrea (Avtor)
ID Dragičević, Oliver (Avtor)
ID Kovač, Vjekoslav (Avtor)
ID Škreb, Kristina Ana (Avtor) |
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| Datoteke: |  URL - Izvorni URL, za dostop obiščite https://www.sciencedirect.com/science/article/pii/S0001870823003821
 PDF - Predstavitvena datoteka, prenos (1,10 MB)
MD5: 8B1845458CDDCA277D057F58DBE69B2E
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | We prove a dimension-free $L^p(\Omega)\times L^q(\Omega)\times L^r(\Omega)\rightarrow L^1(\Omega\times (0,\infty))$ embedding for triples of elliptic operators in divergence form with complex coefficients and subject to mixed boundary conditions on $\Omega$, and for triples of exponents $p,q,r \in (1,\infty)$ mutually related by the identity $1/p+1/q+1/r=1$. Here $\Omega$ is allowed to be an arbitrary open subset of $\mathbb{R}^d$. Our assumptions involving the exponents and coefficient matrices are expressed in terms of a condition known as $p$-ellipticity. The proof utilizes the method of Bellman functions and heat flows. As a corollary, we give applications to (i) paraproducts and (ii) square functions associated with the corresponding operator semigroups, moreover, we prove (iii) inequalities of Kato-Ponce type for elliptic operators with complex coefficients. All the above results are the first of their kind for elliptic divergence-form operators with complex coefficients on arbitrary open sets. Furthermore, the approach to (ii),(iii) through trilinear embeddings seems to be new. |
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| Ključne besede: | elliptic differential operator, p-ellipticity, operator semigroup, multilinear estimate |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.10.2023 |
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| Leto izida: | 2023 |
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| Št. strani: | 72 str. |
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| Številčenje: | Vol. 431, article no. 109239 |
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| PID: | 20.500.12556/DiRROS-18411  |
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| UDK: | 517.9 |
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| ISSN pri članku: | 0001-8708 |
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| DOI: | 10.1016/j.aim.2023.109239 |
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| COBISS.SI-ID: | 177492995 |
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| Opomba: |
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| Datum objave v DiRROS: | 15.03.2024 |
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| Število ogledov: | 454 |
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| Število prenosov: | 235 |
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| Metapodatki: |    |
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