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Inverse problems for elliptic equations with fractional power type nonlinearities

Tony LiimatainenTony LiimatainenTeemu TyniMikko SaloYi-hsuan Lin

subject

Mathematics - Differential GeometryApplied Mathematics010102 general mathematicsType (model theory)Inverse problem01 natural sciencesFractional powerPower (physics)010101 applied mathematicsNonlinear systemMathematics - Analysis of PDEsDifferential Geometry (math.DG)Linearization35R30 35J25 35J61FOS: MathematicsApplied mathematicsOrder (group theory)0101 mathematicsAnalysisLinear equationAnalysis of PDEs (math.AP)Mathematics

description

We study inverse problems for semilinear elliptic equations with fractional power type nonlinearities. Our arguments are based on the higher order linearization method, which helps us to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not known. By using a fractional order adaptation of this method, we show that the results of [LLLS20a, LLLS20b] remain valid for general power type nonlinearities.

yearjournalcountryeditionlanguage
2020-12-09
http://arxiv.org/abs/2012.04944