Estimates of Nonnegative Solutions to Semilinear Elliptic Equations
Khalifa El Mabrouk, Basma Nayli

TL;DR
This paper establishes bounds for nonnegative solutions to certain semilinear elliptic inequalities using a function determined solely by the nonlinearity, independent of the operator or domain.
Contribution
It introduces a universal function that provides lower bounds for solutions of semilinear elliptic inequalities, independent of the specific elliptic operator or domain.
Findings
Derived a universal function that bounds solutions from below.
Established bounds applicable to a wide class of elliptic inequalities.
The bounds depend only on the nonlinearity and the Green function of the source term.
Abstract
Let be a second order uniformly elliptic differential operator in a domain of , be a nondecreasing continuous function and let be locally bounded Borel measurable functions. Under appropriate conditions, we determine a function with values in such that for every nonnegative solution to inequality in and for every , where is the Green function of . The function is completely determined by and does not depend on or .
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Differential Equations and Boundary Problems
