Natural SciencesMathematicsDifferential EquationsDynamical SystemsFluid DynamicsBoundary-value ProblemsOperator TheoryPartial Differential EquationsRegular SolutionsElliptic Partial Differential EquationsExistence ConditionsInterpolation TheoryParabolic Partial Differential EquationsRegularity CriteriaRegularity TheorySobolev Spaces
Abstract Partial differential equations of the form MDtU+LU = f are considered in which M and L denote realizations of regular elliptic linear partial differential operators of respective orders 2 m and 2 l. The abstract existence results of Part I lead to existence of generalized solutions of the equation. Regularity results are obtained by the technique of interpolation theory. The results include the parabolic equation (m = 0) and pseudo-parabolic equations m≧l. The extensive bibliography contains about 36 references to the literature on this class of equations
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Shmuel Agmon, Avron Douglis, Louis Nirenberg · Communications on Pure and Applied Mathematics · 1959 · 3.8K citations
Natural Sciences, Mechanical Engineering, Differential Equations +10
Lectures on Elliptic Boundary Value Problems.
A. Friedman, Shmuel Agmon · American Mathematical Monthly · 1966 · 998 citations