Functional Analytic Methods for Partial Differential Equations
Combining both classical and current methods of analysis, this text present discussions on the application of functional analytic methods in partial differential equations. It furnishes a simplified, self-contained proof of Agmon-Douglis-Niremberg's Lp-estimates for boundary value problems, using the theory of singular integrals and the Hilbert transform.
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adjoint Analogously analytic applying assertion assume assumptions Banach space belonging bounded linear operator called Chapter closed Co-semigroup coefficients Combining complete conclude Consequently consider constant continuous converges D(Ao Definition denote dense depending derivatives desired easily seen element elliptic equal established estimate exists exists a constant finite fixed follows function defined given Hence Hilbert holds homogeneous function implies independent inequality integer kernel Lemma LP(R mapping measurable nonnegative integer norm Noting obtain open set polynomial positive constant Proof Proposition proved Remark replaced respectively result right hand side satisfying semigroup sequence shown solution stable strong strongly sufficiently Suppose term Theorem Theory topology transform Un(t unique value problem view of Lemma view of Theorem virtue write