Mathematical Sciences: Schrodinger Operators and Elliptic   Eigenvalue Problems with an Indefinite Weight Function
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{'SignBlockName': 'William Y. Velez', 'PO_EMAI': None, 'PO_PHON': None}
This research treats spectral theory of Schrodinger                       operators and elliptic boundary value problems with indefinite                  weight functions.   Such eigenvalue problems occur naturally in                 the study of nonlinear partial differential equations and are of                broad interest in mathematical physics and applied mathematics.                 In physics and engineering they arise, for instance, in transport               theory, lasers,  crystal coloration, hydrodynamics, and                         reaction-diffusion.                                                                   Professor Lapidus will conduct research on semilinear                     elliptic equations and the related topic of eigenvalue problems                 with indefinite weight.  The elliptic problems are set on bounded               domains with Dirichlet or Neumann boundary conditions.  He will                 also consider Schrodinger operators on unbounded domains with                   discrete spectrum.  He will investigate both eigenvalues and                    eigenfunctions, with special emphasis on extensions of classical                asymptotic formulas and remainder estimates, distribution of                    eigenvalues, inverse problems, and decay and oscillation of the                 eigenfunctions.
{'FirstName': 'Michel', 'LastName': 'Lapidus', 'PI_MID_INIT': 'L', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Michel L Lapidus', 'EmailAddress': 'lapidus@math.ucr.edu', 'NSF_ID': '000468296', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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