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Let $K \subset Q$ be compact, convex sets in $ℝ^{n}$ with $\overset{\circ}{K} \neq \emptyset$ and let $P (D)$ be a linear, constant coefficient PDO. It is characterized in various ways when each zero solution of $P (D)$ in the space $ℰ (K)$ of all $C^{\infty}$ -functions on $K$ extends to a zero solution in $ℰ (Q)$ resp. in $ℰ (ℝ^{n})$ . The most relevant characterizations are in terms of Phragmén-Lindelöf conditions on the zero variety of $P$ in $ℂ^{n}$ and in terms of fundamental solutions for $P (D)$ with lacunas.

Extension of solutions for Monge-Ampère equations of hyperbolic type

Mikio Tsuji (1996)

Banach Center Publications

Extension of zero-solutions of partial differential operators with dominating principal part.

Uwe Franken (1997)

Journal für die reine und angewandte Mathematik

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Eigencurves for a Steklov problem.

Exceptional sets for solutions to quasilinear parabolic equations in weighted Sobolev spaces.

Existence et prolongement des solutions holomorphes des équations aux dérivées partielles.

Existence of solutions to microhyperbolic boundary value problems

Extension and lacunas of solutions of linear partial differential equations

Extension of solutions for Monge-Ampère equations of hyperbolic type

Extension of zero-solutions of partial differential operators with dominating principal part.

Currently displaying 1 – 7 of 7