In determining the appropriate rate, courts have considered whether, during the period of infringement, the plaintiff “borrowed money at a higher rate, what that rate was, or [whether] there was a causal connection between any borrowing and the loss of the use of the money awarded as a result of [the defendant's] infringement.” Laitram Corp. v. NEC Corp., 115 F.3d 947, 955 (Fed.Cir.1997) (upholding district court's decision to use the Treasury Bill rate in case where district court found no evidence of “a causal connection between any borrowing and the loss of the use of the money awarded as a result of the infringement.”). Such factors would make an award at a higher rate more appropriate.

For "[w]hile a mandate is controlling as to matters within its compass, on the remand a lower court is free as to other issues." Sprague v. Ticonic Nat'l Bank, 307 U.S. 161, 168 (1939) (citing In re Sanford Fork Tool Co., 160 U.S. 247, 256 (1895)); see also Laitram Corp. v. NEC Corp., 115 F.3d 947, 951, 42 USPQ2d 1897, 1900 (Fed. Cir. 1997) ("Upon return of its mandate, the district court cannot give relief beyond the scope of that mandate, but it may act on matters left open by the mandate.") (citations and quotations omitted). The district court found that the Engel III court, by explicitly affirming the validity of the license agreement, implicitly decided that Engel did not have a right to seek a refund of payments under the agreement.

Resolution of those two issues did not require consideration of the doctrine of equivalents. Our recent decision in Laitram Corp. v. NEC Corp., 115 F.3d 947, 42 USPQ2d 1897 (Fed. Cir. 1997), is instructive here. After Laitram won a jury verdict in a patent infringement suit, NEC filed motions for judgment as a matter of law (JMOL) on the issues of infringement, willfulness, and claim identicality.

The mandate rule provides that a district court is foreclosed from considering further issues actually decided on appeal. Amado v. Microsoft Corp., 517 F.3d 1353, 1360 (Fed.Cir.2008) (“The mandate rule provides that ‘issues actually decided [on appeal]—those within the scope of the judgment appealed from, minus those explicitly reserved or remanded by the court—are foreclosed from further consideration’ ”); Engel Industries, Inc. v. Lockformer Co., 166 F.3d 1379, 1383 (Fed.Cir.1999) (“Unless remanded, all issues within the scope of the appealed judgment are deemed incorporated within the mandate and thus are precluded from further adjudication”); Laitram Corp. v. NEC Corp., 115 F.3d 947, 951 (Fed.Cir.1997) (issues that the court of appeals has decided explicitly or by necessary implication may not be reexamined by the district court). The district court is free on remand, however, to consider issues outside the scope of the mandate.

[E]very appellate court judgment vests jurisdiction in the district court to carry out some further proceedings. . . . [T]he nature of the district court's remaining tasks is discerned not simply from the language of the judgment, but from the judgment in combination with the accompanying opinion." Exxon Chem. Patents, Inc. v. Lubrizol Corp. (Exxon Chem.), 137 F.3d 1475, 1483 (Fed. Cir. 1998) (citing In re Sanford Fork Tool Co., 160 U.S. 247, 256, 16 S.Ct. 291, 40 L.Ed. 414 (1895) and Laitram Corp. v. NEC Corp. (Laitram), 115 F.3d 947, 952 (Fed. Cir. 1997)). The general rule is that a trial court is "free to take any action that is consistent with the appellate mandate, as informed by both the formal judgment issued by the court and the court's written opinion."

"[T]he opinion delivered by this court at the time of rendering its decree may be consulted to ascertain what was intended by its mandate." Laitram Corp. v. NEC Corp., 115 F.3d 947, 952 (Fed. Cir. 1997) (quoting In re Sanford Fork & Tool Co., 160 U.S. 247, 256 (1895)). "Unless remanded by this court, all issues within the scope of the appealed judgment are deemed incorporated within the mandate and thus are precluded from further adjudication."

While the district court may not grant relief beyond the scope of the Federal Circuit's mandate, it may act on matters left open by the mandate. Laitram Corp. v. NEC Corp., 115 F.3d 947, 951 (Fed. Cir. 1997); see also Exxon Corp. v. United States, 931 F.2d 874, 877 (Fed. Cir. 1991) (law-of-the-case doctrine does not constrain the trial court with respect to issues it previously decided that were not also decided by the appellate court's judgment). It is doubtful that the Federal Circuit's single statement that it was affirming in part and modifying in part this court's claim construction, see 381 F.3d at 1374, meant that its judgment decided all claim construction issues, since these issues were not appealed by the parties nor discussed by the court.

The law of the case doctrine is applicable both to issues decided explicitly and to issues decided "by necessary implication." Laitram Corp. v. NEC Corp., 115 F.3d 947, 951 (Fed. Cir. 1997).

"[E]very appellate court judgment vests jurisdiction in the district court to carry out some further proceedings. . . . [T]he nature of the district court's remaining tasks is discerned not simply from the language of the judgment, but from the judgment in combination with the accompanying opinion." Exxon Chem. Patents, Inc. v. Lubrizol Corp. (Exxon Chem.), 137 F.3d 1475, 1483 (Fed. Cir. 1998) (citing In re Sanford Fork Tool Co., 160 U.S. 247, 256 (1895) and Laitram Corp. v. NEC Corp. (Laitram), 115 F.3d 947, 952 (Fed. Cir. 1997)). The general rule is that a trial court is "free to take any action that is consistent with the appellate mandate, as informed by both the formal judgment issued by the court and the court's written opinion."

Amado v. Microsoft Corp. , 517 F.3d 1353, 1360 (Fed. Cir. 2008) (alteration in original) (quoting Engel Indus., Inc. v. Lockformer Co. , 166 F.3d 1379, 1383 (Fed. Cir. 1999) ). "We review the district court's interpretation of our mandate de novo under Federal Circuit law." Metso Mins. Inc. v. Terex Corp. , 594 F. App'x 649, 651 (Fed. Cir. 2014) (citing TecSec, Inc. v. Int'l Bus. Machs. Corp. , 731 F.3d 1336, 1341 (Fed. Cir. 2013) ); see Cardiac Pacemakers, Inc. v. St. Jude Med., Inc. , 576 F.3d 1348, 1355–56 (Fed. Cir. 2009) ; Engel , 166 F.3d at 1382 ; Laitram Corp. v. NEC Corp. , 115 F.3d 947, 950–51 (Fed. Cir. 1997). In interpreting this court's mandate, "both the letter and the spirit of the mandate must be considered."