We introduce a condition on accretive matrix functions, called p-ellipticity, and discuss its applications to the Lp theory of elliptic PDEs with complex coefficients. Our examples are: (i) generalized convexity of power functions (Bellman functions), (ii) dimension-free bilinear embeddings, (iii) Lp-contractivity of semigroups, and (iv) holomorphic functional calculus. Recent work by Dindoš and Pipher established close ties between p-ellipticity and (v) regularity theory of elliptic PDEs with complex coefficients. The p-ellipticity condition arises from studying uniform positivity of a quadratic form associated with the matrix in question on the one hand, and the Hessian of a power function on the other. Our results regarding contractivity extend earlier theorems by Cialdea and Maz’ya.

Convexity of power functions and bilinear embedding for divergence-form operators with complex coefficients

A. Carbonaro;
2020-01-01

Abstract

We introduce a condition on accretive matrix functions, called p-ellipticity, and discuss its applications to the Lp theory of elliptic PDEs with complex coefficients. Our examples are: (i) generalized convexity of power functions (Bellman functions), (ii) dimension-free bilinear embeddings, (iii) Lp-contractivity of semigroups, and (iv) holomorphic functional calculus. Recent work by Dindoš and Pipher established close ties between p-ellipticity and (v) regularity theory of elliptic PDEs with complex coefficients. The p-ellipticity condition arises from studying uniform positivity of a quadratic form associated with the matrix in question on the one hand, and the Hessian of a power function on the other. Our results regarding contractivity extend earlier theorems by Cialdea and Maz’ya.
File in questo prodotto:
File Dimensione Formato  
CarbonaroDragicevicJEMS170725v3.pdf

accesso aperto

Tipologia: Documento in Post-print
Dimensione 496.44 kB
Formato Adobe PDF
496.44 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/961411
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 7
social impact