Determining a Pair of Metrics by Boundary Energy Associat edtoa Multitime PDE System
Keywords:
potentialmap,leastsquaresLagrangian,boundaryenergy,multi-raytransform,extremalsAbstract
Our theory of dete rminingatensor byboundar yenergy of amultiti mefirstorder PDE system issimilartothosedevelopedby Sharafutdinov.Section1refinesthetheoryofpotentialmapsdetermined byafirstordermultitime PDEsystemandaverticalmetric.Section2definestheboundaryenergy ofafirstorder PDEsystemandprovesthattheproblemofdeterminingaverticalmetricfromthe boundaryenergyofamultitime PDE systemcannothaveauniquesolution. Section3linearizesthe abovementionedproblemanddefinesthenotionofmulti-raytransform.
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