scholarly journals Density of smooth functions in variable exponent Sobolev spaces

2015 ◽  
Vol 127 ◽  
pp. 196-205 ◽  
Author(s):  
Thanasis Kostopoulos ◽  
Nikos Yannakakis
Keyword(s):  
Sobolev Spaces ◽  
Variable Exponent ◽  
Smooth Functions ◽  
Variable Exponent Sobolev Spaces

scholarly journals Density of smooth functions between two manifolds in Sobolev spaces

1988 ◽  
Vol 80 (1) ◽  
pp. 60-75 ◽  
Author(s):  
Fabrice Bethuel ◽  
Xiaomin Zheng
Keyword(s):  
Sobolev Spaces ◽  
Smooth Functions

Density of smooth functions in weighted Sobolev spaces

2013 ◽  
Vol 88 (3) ◽  
pp. 669-673 ◽  
Author(s):  
V. V. Zhikov
Keyword(s):  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Smooth Functions

Time-fractional diffusion equation in the fractional Sobolev spaces

2015 ◽  
Vol 18 (3) ◽  
Author(s):  
Rudolf Gorenflo ◽  
Yuri Luchko ◽  
Masahiro Yamamoto
Keyword(s):  
Diffusion Equation ◽  
Sobolev Spaces ◽  
Caputo Derivative ◽  
Fractional Integration ◽  
Time Derivative ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Fractional Sobolev Spaces ◽  
Smooth Functions ◽  
Time Fractional Diffusion Equation

AbstractThe Caputo time-derivative is usually defined pointwise for well-behaved functions, say, for the continuously differentiable functions. Accordingly, in the publications devoted to the theory of the partial fractional differential equations with the Caputo derivatives, the functional spaces where the solutions are looked for are often the spaces of smooth functions that appear to be too narrow for several important applications. In this paper, we propose a definition of the Caputo derivative on a finite interval in the fractional Sobolev spaces and investigate it from the operator theoretic viewpoint. In particular, some important equivalences of the norms related to the fractional integration and differentiation operators in the fractional Sobolev spaces are given. These results are then applied for proving the maximal regularity of the solutions to some initial-boundary-value problems for the time-fractional diffusion equation with the Caputo derivative in the fractional Sobolev spaces.

On a class of weighted Sobolev spaces and the minimization of quadratic forms

1978 ◽  
Vol 81 (1-2) ◽  
pp. 119-130
Author(s):  
Frans Penning ◽  
Niko Sauer
Keyword(s):  
Weight Function ◽  
Sobolev Spaces ◽  
Compact Support ◽  
Quadratic Forms ◽  
Weighted Sobolev Spaces ◽  
Weight Functions ◽  
Compact Embedding ◽  
Embedding Theorems ◽  
Smooth Functions ◽  
Square Integrability

SynopsisIn this paper a class of weighted Sobolev spaces defined in terms of square integrability of the gradient multiplied by a weight function, is studied. The domain of integration is either the spaceRnor a half-space ofRn. Conditions on the weight functions that will ensure density of classes of smooth functions or functions with compact support, and compact embedding theorems, are derived. Finally the results are applied to a class of isoperimetrical problems in the calculus of variations in which the domain of integration is unbounded.

Widths of classes of finitely smooth functions in Sobolev spaces

2005 ◽  
Vol 77 (3-4) ◽  
pp. 494-498 ◽  
Author(s):  
S. N. Kudryavtsev
Keyword(s):  
Sobolev Spaces ◽  
Smooth Functions
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