Global regularity for solutions of the minimal surface equation with continuous boundary values
Green's theorem from the viewpoint of applications
Making use of a line integral defined without use of the partition of unity, Green’s theorem is proved in the case of two-dimensional domains with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces
Hadamard-type inequalities for quasiconvex functions.
Hake's property of a multidimensional generalized Riemann integral
Hamiltoniens quasi-convexes quasi-concaves
Harmonic analysis of the space BV.
We establish new results on the space BV of functions with bounded variation. While it is well known that this space admits no unconditional basis, we show that it is almost characterized by wavelet expansions in the following sense: if a function f is in BV, its coefficient sequence in a BV normalized wavelet basis satisfies a class of weak-l1 type estimates. These weak estimates can be employed to prove many interesting results. We use them to identify the interpolation spaces between BV and Sobolev...
Harmonic sum and duality.
Harnachk Inequalities for Solutions of General Second Order Parabolic Equations and Estimates of Their Hölder Constants.
Hausdorff measures of the set of critical values of functions of the class
Henstock-Kurzweil integral on sets
The generalized Riemann integral of Pfeffer (1991) is defined on all bounded subsets of , but it is additive only with respect to pairs of disjoint sets whose closures intersect in a set of -finite Hausdorff measure of codimension one. Imposing a stronger regularity condition on partitions of sets, we define a Riemann-type integral which satisfies the usual additivity condition and extends the integral of Pfeffer. The new integral is lipeomorphism-invariant and closed with respect to the formation...
Hermite-Hadamard type inequalities for increasing radiant functions.
Hermite-Hadamard-type inequalities for generalized convex functions.
Hessian determinants as elements of dual Sobolev spaces
In this short note we present new integral formulas for the Hessian determinant. We use them for new definitions of Hessian under minimal regularity assumptions. The Hessian becomes a continuous linear functional on a Sobolev space.
Hidden structures in the class of convex functions and a new duality transform
Our main intention in this paper is to demonstrate how some seemingly purely geometric notions can be presented and understood in an analytic language of inequalities and then, with this understanding, can be defined for classes of functions and reveal new and hidden structures in these classes. One main example which we discovered is a new duality transform for convex non-negative functions on attaining the value 0 at the origin (which we call “geometric convex functions”). This transform, together...
Higher integrability of determinants and weak convergence in L1.
Homogeneous aggregation operators
Recently, the utilization of invariant aggregation operators, i.e., aggregation operators not depending on a given scale of measurement was found as a very current theme. One type of invariantness of aggregation operators is the homogeneity what means that an aggregation operator is invariant with respect to multiplication by a constant. We present here a complete characterization of homogeneous aggregation operators. We discuss a relationship between homogeneity, kernel property and shift-invariance...
Homogeneous means and some functional equations
Hyperlogarithmic expansion and the volume of a hyperbolic simplex
Ill-posedness of the Cauchy problem for totally degenerate system of conservation laws.
Ilmanen’s lemma on insertion of C functions