Research Summary
نویسنده
چکیده
1. Overview 2 2. Electromagnetic waves 3 2.1. Approximate cloaking via change of variables 3 2.1.1. Cloaking for the Helmholtz equation 3 2.1.2. Full range estimates for the degree of invisibility 4 2.1.3. Perfect cloaking for the Helmholtz equation 4 2.2. Electrical impedance tomography 5 2.3. Generalized impedance boundary conditions 5 2.3.1. The Helmholtz equation 6 2.3.1. The time harmonic Maxwell equations 6 3. The topological degree and liftings 6 3.1. A new estimate for the topological degree 6 3.2. The optimal constant in the new estimate for the degree 6 3.3. Some inequalities related to liftings and applications 6 4. Sobolev spaces 7 4.1. Characterizations of Sobolev spaces 7 4.2. Some new inequalities in Sobolev spaces 8 4.3. Gamma-convergence, Sobolev norms, and BV functions 8 4.4. On a new class of functions related to VMO 8 5. The distributional Jacobian 9 5.1. The distributional Jacobian of maps from the sphere Sd into it self 9 5.2. The Jacobian determinant 9 6. The calculus of variations: thin membranes and d-cones 10 7. Differential equations: the peak time in some pharmacodynamic models 11 7.1. Monotonicity of the peak time in turn over models 11 7.2. The peak time in the Pool-Precursor Model 11 References 12
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