Hard implicit function theorem and small periodic solutions to partial differential equations
Harnack inequalities for evolving hypersurfaces.
Higher asymptotics of the complex Monge-Ampère equation
Higher integrability for weak solutions of higher order degenerate parabolic systems.
High-order mixed-type differential equations with weighted integral boundary conditions.
Hölder regularity in non autonomous degenerate abstract parabolic equations
Homogeneous two-point problem for PDE of the second order in time variable and infinite order in spatial variables
We prove that homogeneous problem for PDE of second order in time variable, and generally infinite order in spatial variables with local two-point conditions with respect to time variable, has only trivial solution in the case when the characteristic determinant of the problem is nonzero. In another, opposite case, we prove the existence of nontrivial solutions of the problem, and we propose a differential-symbol method of constructing them.
How many are affine connections with torsion
The question how many real analytic affine connections exist locally on a smooth manifold of dimension is studied. The families of general affine connections with torsion and with skew-symmetric Ricci tensor, or symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of variables.
How many are equiaffine connections with torsion
The question how many real analytic equiaffine connections with arbitrary torsion exist locally on a smooth manifold of dimension is studied. The families of general equiaffine connections and with skew-symmetric Ricci tensor, or with symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of variables.
Hypoellipticité d'équations aux dérivées partielles non linéaires
Hypoellipticité et hyperfonctions