Halbgruppen und semilineare Anfangs-Randwertprobleme.
Hamilton-Jacobi equations for control problems of parabolic equations
We study Hamilton-Jacobi equations related to the boundary (or internal) control of semilinear parabolic equations, including the case of a control acting in a nonlinear boundary condition, or the case of a nonlinearity of Burgers' type in 2D. To deal with a control acting in a boundary condition a fractional power – where (A,D(A)) is an unbounded operator in a Hilbert space X – is contained in the Hamiltonian functional appearing in the Hamilton-Jacobi equation. This situation has already...
Hardy inequalities and dynamic instability of singular Yamabe metrics
Hardy spaces of conjugate temperatures
We define Hardy spaces of pairs of conjugate temperatures on using the equations introduced by Kochneff and Sagher. As in the holomorphic case, the Hilbert transform relates both components. We demonstrate that the boundary distributions of our Hardy spaces of conjugate temperatures coincide with the boundary distributions of Hardy spaces of holomorphic functions.
Harmonic and quasi-harmonic spheres, part III. Rectifiablity of the parabolic defect measure and generalized varifold flows
Harmonic averages, exact difference schemes and local Green’s functions in variable coefficient PDE problems
A brief survey is given to show that harmonic averages enter in a natural way in the numerical solution of various variable coefficient problems, such as in elliptic and transport equations, also of singular perturbation types. Local Green’s functions used as test functions in the Petrov-Galerkin finite element method combined with harmonic averages can be very efficient and are related to exact difference schemes.
Harnachk Inequalities for Solutions of General Second Order Parabolic Equations and Estimates of Their Hölder Constants.
Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations
In this work we prove both local and global Harnack estimates for weak supersolutions to second order nonlinear degenerate parabolic partial differential equations in divergence form. We reduce the proof to an analysis of so-called hot and cold alternatives, and use the expansion of positivity together with a parabolic type of covering argument. Our proof uses only the properties of weak supersolutions. In particular, no comparison to weak solutions is needed.
Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations
Harnack inequalities for curvature flows depending on mean curvature.
Harnack inequalities for evolving hypersurfaces.
Harnack inequality and heat kernel estimates for the Schrödinger operator with Hardy potential
In this preliminary Note we outline some results of the forthcoming paper [11], concerning positive solutions of the equation . A parabolic Harnack inequality is proved, which in particular implies a sharp two-sided estimate for the associated heat kernel. Our approach relies on the unitary equivalence of the Schrödinger operator with the opposite of the weighted Laplacian when .
Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term.
Harnack's estimates: positivity and local behavior of degenerate and singular parabolic equations.
Harnack's inequality for parabolic operators with singular low order terms.
Heat distribution in a medium with concentrated perturbation of density.
Heat Equation and the Volume of Tubes.
Heat flow and boundary value problem for harmonic maps
Heat flow, brownian motion and newtonian capacity
Heat Flow out of Regions in IRm.