Sobolev and isoperimetric inequalities for degenerate metrics.
Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces
We prove local embeddings of Sobolev and Morrey type for Dirichlet forms on spaces of homogeneous type. Our results apply to some general classes of selfadjoint subelliptic operators as well as to Dirichlet operators on certain self-similar fractals, like the Sierpinski gasket. We also define intrinsic BV spaces and perimeters and prove related isoperimetric inequalities.
Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces
Our aim in this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on grand Morrey spaces of variable exponents over non-doubling measure spaces. As an application of the boundedness of the maximal operator, we establish Sobolev's inequality for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces. We are also concerned with Trudinger's inequality and the continuity for Riesz potentials.
Sobolev embeddings for variable exponent Riesz potentials on metric spaces.
Solution of the Dirichlet problem for the Laplace equation
For open sets with a piecewise smooth boundary it is shown that a solution of the Dirichlet problem for the Laplace equation can be expressed in the form of the sum of the single layer potential and the double layer potential with the same density, where this density is given by a concrete series.
Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. II
Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. I
Solution of the Neumann problem for the Laplace equation
For fairly general open sets it is shown that we can express a solution of the Neumann problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series. If the open set is simply connected and bounded then the solution of the Dirichlet problem is the double layer potential with a density given by a similar series.
Solution of the Robin problem for the Laplace equation
For open sets with a piecewise smooth boundary it is shown that we can express a solution of the Robin problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series.
Solutions of DEs and PDEs as potential maps using first order Lagrangians.
Solutions positives et mesure harmonique pour des opérateurs paraboliques dans des ouverts «lipschitziens»
Soit un opérateur parabolique sur écrit sous forme divergence et à coefficients lipschitziens relativement à une métrique adaptée. Nous cherchons à comparer près de la frontière le comportement relatif des -solutions positives sur un domaine “lipschitzien”. Dans un premier temps, nous démontrons un principe de Harnack uniforme pour certaines -solutions positives. Ce principe nous permet alors de démontrer une inégalité de Harnack forte à la frontière pour certains couples de -solutions positives....
Solvability Conditions for a Linearized Cahn-Hilliard Equation of Sixth Order
We obtain solvability conditions in H6(ℝ3) for a sixth order partial differential equation which is the linearized Cahn-Hilliard problem using the results derived for a Schrödinger type operator without Fredholm property in our preceding article [18].
Solvability of the Poisson equation in weighted Sobolev spaces
The aim of this paper is to prove the existence of solutions to the Poisson equation in weighted Sobolev spaces, where the weight is the distance to some distinguished axis, raised to a negative power. Therefore we are looking for solutions which vanish sufficiently fast near the axis. Such a result is useful in the proof of the existence of global regular solutions to the Navier-Stokes equations which are close to axially symmetric solutions.
Solving Fractional Diffusion-Wave Equations Using a New Iterative Method
Mathematics Subject Classification: 26A33, 31B10In the present paper a New Iterative Method [1] has been employed to find solutions of linear and non-linear fractional diffusion-wave equations. Illustrative examples are solved to demonstrate the efficiency of the method.* This work has partially been supported by the grant F. No. 31-82/2005(SR) from the University Grants Commission, N. Delhi, India.
Solving -Laplacian equations on complete manifolds.
Solving the Degenerate Complex Monge-Ampère Equation with One Concentrated Singularity.
Some analytic aspects of probabilistic potential theory
Some applications of generalized condensers in the theory of analytic functions.
Some applications of the trace condition for pluriharmonic functions in Cn.
In this paper we investigate some applications of the trace condition for pluriharmonic functions on a smooth, bounded domain in Cn. This condition, related to the normal component on ∂D of the ∂-operator, permits us to study the Neumann problem for pluriharmonic functions and the ∂-problem for (0,1)-forms on D with solutions having assigned real part on the boundary.
Some Caccioppoli estimates for differential forms.