Generation of Analytic Semigroups by Strongly Elliptic Operators Under General Boundary Conditions

1 May 1980

journal article
Published by JSTOR in Transactions of the American Mathematical Society

Vol. 259 (1) , 299-310
https://doi.org/10.2307/1998159

Abstract

Strongly elliptic operators are shown to generate analytic semigroups of evolution operators in the topology of uniform convergence, when realized under general boundary conditions on (possibly) unbounded domains. An application to the existence and regularity of solutions to parabolic initial-boundary value problems is indicated.

Keywords

This publication has 10 references indexed in Scilit:

Spectral theory of heterogeneous diffusion systems
Journal of Mathematical Analysis and Applications, 1976
Generation of Analytic Semigroups by Strongly Elliptic Operators
Transactions of the American Mathematical Society, 1974
On the existence, uniqueness and regularity of solutions to general elliptic boundary-value problems
Journal of Differential Equations, 1974
On Green's functions of elliptic and parabolic boundary value problems
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1972
Lectures on Elliptic Boundary Value Problems.
The American Mathematical Monthly, 1966
Multiple Integrals in the Calculus of Variations
Published by Springer Nature ,1966
On general boundary value problem for parabolic equations
Kyoto Journal of Mathematics, 1964
On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems
Communications on Pure and Applied Mathematics, 1962
On the spectral theory of elliptic differential operators. I
Mathematische Annalen, 1961
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
Communications on Pure and Applied Mathematics, 1959