Spectral theory of nonlinear equations and n-widths of Sobolev spaces

1993 ◽  
pp. 19-30
Author(s):  
A. P. Buslaev ◽  
V. M. Tikhomirov
Keyword(s):  
Spectral Theory ◽  
Nonlinear Equations ◽  
Sobolev Spaces

SPECTRAL THEORY AND EMBEDDINGS OF SOBOLEV SPACES

1979 ◽  
Vol 30 (4) ◽  
pp. 431-453 ◽  
Author(s):  
D. E. EDMUNDS ◽  
W. D. EVANS
Keyword(s):  
Spectral Theory ◽  
Sobolev Spaces

Properties of Equivalent Capacities

1971 ◽  
Vol 14 (1) ◽  
pp. 5-11 ◽  
Author(s):  
R. A. Adams
Keyword(s):  
Partial Differential Equations ◽  
Euclidean Space ◽  
Sobolev Space ◽  
Differential Equations ◽  
Spectral Theory ◽  
Sobolev Spaces ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Closed Set ◽  
Shed Light

Various definitions of capacity of a subset of a domain in Euclidean space have been used in recent times to shed light on the solvability and spectral theory of elliptic partial differential equations and to establish properties of the Sobolev spaces in which these equations are studied. In this paper we consider two definitions of the capacity of a closed set E in a domain G. One of these capacities measures, roughly speaking, the amount by which the set of function in C∞(G) which vanish near E fails to be dense in the Sobolev space Wm, p(G).

Logarithmic Sobolev Spaces and Their Applications to Spectral Theory

1995 ◽  
Vol s3-71 (2) ◽  
pp. 333-371 ◽  
Author(s):  
D. E. Edmunds ◽  
H. Triebel
Keyword(s):  
Spectral Theory ◽  
Sobolev Spaces

scholarly journals Nonlinear equations with a generalized fractional Laplacian

2021 ◽  
Vol 115 (2) ◽  
Author(s):  
Igor Kossowski ◽  
Bogdan Przeradzki
Keyword(s):  
Laplace Operator ◽  
Spectral Theory ◽  
Nonlinear Equations ◽  
Fractional Laplacian ◽  
Existence Results ◽  
Dirichlet Conditions ◽  
Regularity Results

AbstractWe study a generalization of the power of Laplace operator with null Dirichlet conditions by means of the spectral theory and prove several existence results for nonlinear equations with such operators, especially when the problem is resonant. Some regularity results are also obtained.

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