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Showing 1 to 13 of 13 for “"Elliptic Operators"”.
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Determinants of elliptic operators
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1989.
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Obstacle problems with elliptic operators in divergence form
… Ivan Blank, I study the obstacle problem with an elliptic operator in divergence form. First, I give all of the nontrivial details needed to prove a mean value theorem, which was stated by Caffarelli in the Fermi lectures in 1998. In fact, in 1963, Littman, Stampacchia, and Weinberger proved a …
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Critical perturbations of elliptic operators by lower order terms
… solutions of certain boundary value problems for elliptic equations in the upper half-space. More specifically we treat the Dirichlet, Neumann, and Regularity problems for the general second order, linear, elliptic operator under a smallness assumption on the coefficients in certain critical …
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Heat kernel estimates for elliptic operators with Robin boundary conditions
Consider the elliptic operator on a bounded connected open set Ω ⊂ Rd where d ≥ 2, subject to Robin boundary conditions ∂νu + βu = 0. We show that the kernel for the semigroup generated by −A satisfies Gaussian and Hölder Gaussian bounds given domain and coefficients regularities. In particular we …
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Computing Eigenmodes of Elliptic Operators on Manifolds Using Radial Basis Functions
<p>In this work, a numerical approach based on meshless methods is proposed to obtain eigenmodes of Laplace-Beltrami operator on manifolds, and its performance is compared against existing alternative methods. Radial Basis Function (RBF)-based methods allow one to obtain interpolation and …
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Fredholm Properties of a Class of Elliptic Operators on Non-Compact Manifolds
Made available in DSpace on 2014-12-14T13:09:44Z (GMT). No. of bitstreams: 1 8009092.pdf: 2807588 bytes, checksum: 97bc5df25b7ffeaba1b2a40b4b3ed899 (MD5) Previous issue date: 1979
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Extensions of the Cayley-Hamilton Theorem with Applications to Elliptic Operators and Frames.
… can be extended to self-adjoint trace-class operators and to closed self-adjoint operators with trace-class resolvent over a separable Hilbert space. Applications of these results include calculating operators resolvents and finding the inverse of a frame operator.</p>
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Topology of the nodal and critical point sets for eigenfunctions of elliptic operators,
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1971.
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Higher canonical asymptotics of Kähler-Einstein metrics on quasi-projective manifolds
… first develop the analysis of the Monge-Ampere operators on these weighted spaces. We construct a family of linear elliptic operators which can be viewed as certain conjugacies of the specially linearized Monge-Ampbre operators. We derive a theorem of Fredholm alternative for such elliptic …
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Gluing Z₂-Harmonic Spinors on 3-Manifolds
… a detailed analysis of degenerating families of elliptic operators. Part II: This part studies the deformation theory of Z₂-harmonic spinors. For a fixed smooth singular set, the deformation theory of 𝑍₂-harmonic spinors is obstructed by infinite-dimensional cokernel of the semi-Fredholm Z₂-Dirac …
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Topics in harmonic analysis and partial differential equations: extension theorems and geometric maximum principles
… interior pseudo-ball condition, for semi-elliptic operators with singular drift. This, in turn, is used to obtain a sharp version of Hopf's Strong Maximum Principle for second-order, non-divergence form differential operators with singular drift. This part of my thesis originates from a …
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Elliptic problems with small parameter
… and correctness of asymptotic solutions to elliptic differential and pseudodifferential equations. We begin our studies with the case of a general elliptic boundary value problem in partial derivatives. A small parameter enters the coefficients of the main equation as well as into the …
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Matrix probing, skeleton decompositions, and sparse Fourier transform
… Our main application is probing linear operators with smooth pseudodifferential symbols such as the wave equation Hessian in seismic imaging. We also demonstrate numerically that matrix probing can produce good preconditioners for inverting elliptic operators in variable media. Skeleton …