Local bounds, Harnack's inequality and Hölder continuity for divergence type elliptic equations with non-standard growth

• Noemi Wolanski ^[1]
  1. [1] Universidad de Buenos Aires

     Universidad de Buenos Aires

     Argentina

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 56, Nº. 1, 2015, págs. 73-105
• Idioma: inglés
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• Resumen

  • We obtain a Harnack type inequality for solutions to elliptic equations in divergence form with non-standard p(x)-type growth. A model equation is the inhomogeneous p(x)-Laplacian. Namely,Δp(x)u:=div(|∇u|p(x)−2∇u)=f(x)inΩ, for which we prove Harnack's inequality when f∈Lq0(Ω) if max{1,Np1}