Pointwise estimates of solutions to semilinear elliptic equations and inequalities

Abstract

We obtain sharp pointwise estimates for positive solutions to the equation $-Lu+V{u}^q=f$, where $L$ is an elliptic operator in divergence form, $q\in \mathbb{R}\setminus \{0\}$, $f\ge 0$ and $V$ is a function that may change sign, in a domain $\Omega$ in ${\mathbb{R}}^n$, or in a weighted Riemannian manifold.

32 pages, 1 figure

References in corpus (7)

• Elliptic Equations Involving Meausres
• Global estimates for kernels of Neumann series and Green's functions
• Pointwise estimates of solutions to semilinear elliptic equations and inequalities
• Pointwise estimates of solutions to nonlinear equations for nonlocal operators
• A sublinear version of Schur's lemma and elliptic PDE
• Pointwise estimates of Brezis-Kamin type for solutions of sublinear elliptic equations
• Finite energy solutions of quasilinear elliptic equations with sub-natural growth terms

Cited by in corpus (5)

• Pointwise estimates of solutions to nonlinear equations for nonlocal operators
• Pointwise estimates of solutions to semilinear elliptic equations and inequalities
• Positive solutions to Schrödinger's equation and the exponential integrability of the balayage
• Quasilinear elliptic equations with sub-natural growth terms in bounded domains
• Positive solutions and harmonic measure for Schrödinger operators in uniform domains