16 research outputs found
Estimation of Sobolev-type embedding constant on domains with minimally smooth boundary using extension operator
Get PDFStudies on verified computation for solutions to systems of linear and semilinear elliptic partial differential equations
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Numerical verification method for positivity of solutions to elliptic equations (Numerical Analysis : New Developments for Elucidating Interdisciplinary Problems II)
Get PDFIn this paper, we propose a numerical method for verifying the positivity of solutions to semilinear elliptic equations. We provide a sufficient condition for a solution to an elliptic equation to be positive in the domain of the equation, which can be checked numerically without requiring a complicated computation. We present some numerical examples
