Characterization of interpolation spaces and regularity properties for holomorphic semigroups

1989 ◽  
Vol 38 (1) ◽  
pp. 179-187 ◽  
Author(s):  
Gabriella Di Blasio
Keyword(s):  
Interpolation Spaces ◽  
Holomorphic Semigroups ◽  
Regularity Properties

A characterization of the interpolation spaces ofH 1 andL ∞ on the line

1988 ◽  
Vol 4 (1) ◽  
pp. 199-209 ◽  
Author(s):  
Robert Sharpley
Keyword(s):  
Interpolation Spaces

scholarly journals A new characterization of the interpolation spaces between $L^p$ and $L^q$

1984 ◽  
Vol 55 ◽  
pp. 253 ◽  
Author(s):  
Jonathan Arazy ◽  
Michael Cwikel
Keyword(s):  
Interpolation Spaces

Fractional diffusion-wave equations: Hidden regularity for weak solutions

2021 ◽  
Vol 24 (4) ◽  
pp. 1015-1034
Author(s):  
Paola Loreti ◽  
Daniela Sforza
Keyword(s):  
Fractional Derivative ◽  
Weak Solutions ◽  
Caputo Fractional Derivative ◽  
Wave Equations ◽  
Regularity Result ◽  
Fractional Diffusion ◽  
Interpolation Spaces ◽  
Diffusion Wave ◽  
Regularity Properties

Abstract We prove a “hidden” regularity result for weak solutions of time fractional diffusion-wave equations where the Caputo fractional derivative is of order α ∈ (1, 2). To establish such result we analyse the regularity properties of the weak solutions in suitable interpolation spaces.

scholarly journals A Characterization of the Spaces $\mathfrak{S}_{{1/{k + 1}}}^{{k /{k + 1}}} $ by Means of Holomorphic Semigroups

1983 ◽  
Vol 14 (6) ◽  
pp. 1180-1186 ◽  
Author(s):  
S. J. L. van Eijndhoven ◽  
J. de Graaf ◽  
R. S. Pathak
Keyword(s):  
Holomorphic Semigroups

scholarly journals Quasilinear elliptic equations with sub-natural growth and nonlinar potentials

2015 ◽  
Author(s):  
◽  
Dat Tien Cao
Keyword(s):  
Sufficient Conditions ◽  
Finite Energy ◽  
Quasilinear Elliptic Equations ◽  
Natural Growth ◽  
Estimates Of Solutions ◽  
Regularity Properties ◽  
Nonlinear Potentials ◽  
Necessary And Sufficient ◽  
Quasilinear Elliptic

Necessary and sufficient conditions for the existence of finite energy and weak solutions are given. Sharp global pointwise estimates of solutions are obtained as well. We also discuss the uniqueness and regularity properties of solutions. As a consequence, characterization of solvability of the equations with singular natural growth in the gradient terms is deduced. Our main tools are Wolff potential estimates, dyadic models, and related integral inequalities. Special nonlinear potentials of Wolff type ssociated with "sublinear" problems are constructed to obtain sharp bounds of solutions. We also treat equations with the fractional Laplacians. Our approach is applicable to more general quasilinear A-Laplace operators as well as the fully nonlinear k-Hessian operators.

Qualitative Properties of Solutions of m-Laplace Systems

2005 ◽  
Vol 5 (2) ◽  
Author(s):  
Lucio Damascelli ◽  
Berardino Sciunzi
Keyword(s):  
Geometric Characterization ◽  
Qualitative Properties ◽  
Regularity Properties ◽  
Critical Sets ◽  
Regularity Results ◽  
Qualitative Properties Of Solutions

AbstractWe prove regularity results for the solutions of the equation -Δand we prove regularity properties of the solutions as well as qualitative properties of the solutions. Moreover we get a geometric characterization of the critical sets Z

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