Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term.
Harnack inequality for the Schrödinger problem relative to strongly local Riemannian -homogeneous forms with a potential in the Kato class.
Harnack type estimates for nonlinear elliptic systems and applications
Harnack's estimates: positivity and local behavior of degenerate and singular parabolic equations.
Harnack’s inequalities for solutions to the mean curvature equation and to the capillarity problem
Harnack's Inequality for Elliptic Differential Equations on Minimal Surfaces.
Harnack's inequality for parabolic operators with singular low order terms.
Harnack's inequality for quasilinear elliptic equations with coefficients in Morrey spaces
Harnack's inequality for solutions of some degenerate elliptic equations.
We prove Harnack's inequality for non-negative solutions of some degenerate elliptic operators in divergence form with the lower order term coefficients satisfying a Kato type contition.
Heat distribution in a medium with concentrated perturbation of density.
Heat kernel and semigroup estimates for sublaplacians with drift on Lie groups.
Let G be a Lie group. The main new result of this paper is an estimate in L2 (G) for the Davies perturbation of the semigroup generated by a centered sublaplacian H on G. When G is amenable, such estimates hold only for sublaplacians which are centered. Our semigroup estimate enables us to give new proofs of Gaussian heat kernel estimates established by Varopoulos on amenable Lie groups and by Alexopoulos on Lie groups of polynomial growth.
Heat kernel estimates for a class of higher order operators on Lie groups
Let G be a Lie group of polynomial volume growth. Consider a differential operator H of order 2m on G which is a sum of even powers of a generating list of right invariant vector fields. When G is solvable, we obtain an algebraic condition on the list which is sufficient to ensure that the semigroup kernel of H satisfies global Gaussian estimates for all times. For G not necessarily solvable, we state an analytic condition on the list which is necessary and sufficient for global Gaussian estimates....
Hessian measures. II.
Heteroclinic connections of stationary solutions of scalar reaction-diffusion equations
Heteroclinic orbits, mobility parameters and stability for thin film type equations.
Heteroclinic points of multi-dimensional dynamical systems.
Hidden regularity for semilinear hyperbolic partial differential equations
High frequency asymptotic solutions of the reduced wave equation on infinite regions with nonconvex boundaries.
High order regularity for subelliptic operators on Lie groups of polynomial growth.
Let G be a Lie group of polynomial volume growth, with Lie algebra g. Consider a second-order, right-invariant, subelliptic differential operator H on G, and the associated semigroup St = e-tH. We identify an ideal n' of g such that H satisfies global regularity estimates for spatial derivatives of all orders, when the derivatives are taken in the direction of n'. The regularity is expressed as L2 estimates for derivatives of the semigroup, and as Gaussian bounds for derivatives of the heat kernel....
High order transmission conditions for thin conductive sheets in magneto-quasistatics
We propose transmission conditions of order 1, 2 and 3 approximating the shielding behaviour of thin conducting curved sheets for the magneto-quasistatic eddy current model in 2D. This model reduction applies to sheets whose thicknesses ε are at the order of the skin depth or essentially smaller. The sheet has itself not to be resolved, only its midline is represented by an interface. The computation is directly in one step with almost no additional cost. We prove the well-posedness w.r.t. to...