Bounded weak solutions with Orlicz space data: an overview

2024/10/22 by Cruz-Uribe, David
#35B45 #35D30 #35J25 #46E30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.17054

Abstract

It is well known that non-negative solutions to the Dirichlet problem Δu =f in a bounded domain Ω, where f∈ L^q(Ω), q>\fracn2, satisfy ‖u‖_L^∞(Ω) ≤ C‖f‖_L^q(Ω). We generalize this result by replacing the Laplacian with a degenerate elliptic operator, and we show that we can take the data f in an Orlicz space L^A(Ω) that, in the classical case, lies strictly between L^(n)/(2)(Ω) and L^q(Ω), q>\fracn2.

Related

• Bounded weak solutions to elliptic PDE with data in Orlicz spaces
• Elliptic problems with growth in nonreflexive Orlicz spaces and with measure or L¹ data
• Nonlinear Boundary Value Problems via Minimization on Orlicz-Sobolev Spaces
• Local second order regularity of solutions to elliptic Orlicz-Laplace equation
• Orlicz-Sobolev inequalities and the Dirichlet problem for infinitely degenerate elliptic operators