Interior  L p -estimates and local  A p -weights

Isoldo Cardoso ^[2] ; Pablo Viola ^[3] ; Beatriz Viviani ^[1]
1. [1] Universidad Nacional del Litoral
  
  Universidad Nacional del Litoral
  
  Argentina
2. [2] Universidad Nacional de Rosario
  
  Universidad Nacional de Rosario
  
  Argentina
3. [3] Universidad Nacional del Centro de la Provincia de Buenos Aires, Argentina
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Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 59, Nº. 1, 2018, págs. 73-98
Idioma: inglés
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Resumen
- Let Ω be a nonempty open proper and connected subset of Rn, n≥3. Consider the elliptic Schrödinger type operator LEu=AEu+Vu=−Σijaij(x)uxixj+Vu in Ω, and the linear parabolic operator LPu=APu+Vu= ut−Σaij(x,t)uxixj+Vu in ΩT=Ω×(0,T), where the coefficients aij∈VMO and the potential V satisfies a reverse Hölder condition. The aim of this paper is to obtain a priori estimates for the operators LE and LP in weighted Sobolev spaces involving the distance to the boundary and weights in a local Ap class.