Global pointwise estimates of positive solutions to sublinear equations

2022/03/04 by Verbitsky, Igor E.
#42B37 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 31B15 #Secondary 35J61

paper · doi:10.48550/arxiv.2203.02531

Abstract

We give bilateral pointwise estimates for positive solutions u to the sublinear integral equation u = G(σu^q) + f \textrmin Ω, for 0 < q < 1, where σ≥ 0 is a measurable function, or a Radon measure, f ≥ 0, and G is the integral operator associated with a positive kernel G on Ω×Ω. Our main results, which include the existence criteria and uniqueness of solutions, hold for quasi-metric, or quasi-metrically modifiable kernels G. As a consequence, we obtain bilateral estimates, along with the existence and uniqueness, for positive solutions u, possibly unbounded, to sublinear elliptic equations involving the fractional Laplacian, (-Δ)^\fracα2 u = σu^q + μ \textrmin Ω, u=0 \textrmin Ω^c, where 0

Related

• Nonlinear potential estimates for sublinear problems with applications to elliptic semilinear and quasilinear equations
• Elliptic equations involving general subcritical source nonlinearity and measures
• Bilateral estimates of solutions to quasilinear elliptic equations with sub-natural growth terms
• Positive solutions and harmonic measure for Schr "odinger operators in\n uniform domains
• The Dirichlet problem for sublinear elliptic equations with source