| Naslov: | Trilinear embedding for divergence-form operators with complex coefficients |
|---|
| Avtorji: | ID Carbonaro, Andrea (Avtor)
ID Dragičević, Oliver (Avtor)
ID Kovač, Vjekoslav (Avtor)
ID Škreb, Kristina Ana (Avtor) |
|---|
| Datoteke: |  URL - Izvorni URL, za dostop obiščite https://www.sciencedirect.com/science/article/pii/S0001870823003821
 PDF - Predstavitvena datoteka, prenos (1,10 MB)
MD5: 8B1845458CDDCA277D057F58DBE69B2E
|
|---|
| Jezik: | Angleški jezik |
|---|
| Tipologija: | 1.01 - Izvirni znanstveni članek |
|---|
| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
|
|---|
| 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. |
|---|
| Ključne besede: | elliptic differential operator, p-ellipticity, operator semigroup, multilinear estimate |
|---|
| Status publikacije: | Objavljeno |
|---|
| Verzija publikacije: | Objavljena publikacija |
|---|
| Datum objave: | 01.10.2023 |
|---|
| Leto izida: | 2023 |
|---|
| Št. strani: | 72 str. |
|---|
| Številčenje: | Vol. 431, article no. 109239 |
|---|
| PID: | 20.500.12556/DiRROS-18411  |
|---|
| UDK: | 517.9 |
|---|
| ISSN pri članku: | 0001-8708 |
|---|
| DOI: | 10.1016/j.aim.2023.109239 |
|---|
| COBISS.SI-ID: | 177492995 |
|---|
| Opomba: |
|
|---|
| Datum objave v DiRROS: | 15.03.2024 |
|---|
| Število ogledov: | 91 |
|---|
| Število prenosov: | 51 |
|---|
| Metapodatki: |     |
|---|
|
:
|
Kopiraj citat |
|---|
| | | | Objavi na: |  |
|---|
Postavite miškin kazalec na naslov za izpis povzetka. Klik na naslov izpiše
podrobnosti ali sproži prenos. |
