Varopoulos extensions of boundary functions in Lp and BMO in domains with Ahlforsregular boundaries and applications

• Autores: Athanasios D Zacharopoulos
• Directores de la Tesis: Michail Mourgoglou (dir. tes.)
• Lectura: En la Universidad del País Vasco - Euskal Herriko Unibertsitatea ( España ) en 2023
• Idioma: inglés
• Programa de doctorado: Programa de Doctorado en Matemáticas y Estadística por la Universidad de La Laguna; la Universidad de Oviedo; la Universidad de Zaragoza; la Universidad del País Vasco/Euskal Herriko Unibertsitatea y la Universidad Pública de Navarra
• Materias:
  • Matemáticas
• Enlaces
  • Tesis en acceso abierto en: ADDI
• Resumen

  • This thesis focuses on the construnction of Varopoulos-type extensions of Lp and BMO boundary functions in rough domains. To be more specific, let Ω⊂ℝn+1 , n≥1, be an open set with s- Ahlfors regular boundary ∂Ω for some 0

    The latter results hold without the additional pointwise John condition assumption. Finally, for elliptic systems of equations in divergence form with merely bounded complex-valued coefficients, we show some connections between the solvability of Poisson problems with interior data in the appropriate Carleson or tent spaces and the solvability of Dirichlet problem with Lp and BMO boundary data.