MURPHY, Circuit Judge.

I. Introduction

In 2012, this court held that the district court abused its discretion when it awarded Appellant Michael Zinna only $8000 in attorney's fees. Zinna v. Congrove, 680 F.3d 1236, 1242 (10th Cir.2012). We remanded the matter to the district court to calculate a reasonable fee. Id. In a separate order, we ruled Zinna was entitled to a reasonable attorney's fee for the appellate proceedings and remanded the matter to the district court to calculate that fee also. On remand, the district court entered two orders — the first awarded Zinna $16,240 in trial fees and the second awarded him $18,687.50 in appellate fees. A judgment for $34,927.50 "for legal services of trial and appellate counsel" was entered on March 15, 2013. Zinna filed a notice of appeal within thirty days of the judgment.

Exercising jurisdiction pursuant to 28 U.S.C. § 1291, we conclude Zinna's notice of appeal was timely as to both aspects of the fee award. We further conclude the district court ignored our mandate, thereby abusing its discretion when it calculated attorney's fees for the trial court proceedings. Zinna's arguments relating to the award of appellate fees are waived due to inadequate briefing. Accordingly, we affirm in part, reverse in part, and remand the matter to the district court for further proceedings.

II. Background

The details of Zinna's underlying lawsuit against Appellee Congrove are more fully set out in our prior opinion and are not relevant to the issues presented in this appeal. 680 F.3d at 1237-39. In summary, after a jury awarded Zinna $1791 as damages for a violation of his First Amendment rights, he sought approximately $503,000 in attorney's fees. Id. at 1239-40. Applying the three-factor test set out in Justice O'Connor's concurrence in Farrar v. Hobby, 506 U.S. 103, 116-22, 113 S.Ct. 566, 121 L.Ed.2d 494 (1992), the district court concluded Zinna's success was merely technical and awarded him a small fraction of the attorney's fees he sought. Id.; see also Lippoldt v. Cole, 468 F.3d 1204, 1222-24 (10th Cir.2006) (applying Farrar factors to determine whether plaintiff achieved only technical success). This court reversed. Id. at 1242. Applying the Farrar factors, we concluded Zinna's success was not merely technical. Id. at 1239-42. Accordingly, we remanded the matter to the district court and ordered the court to calculate a lodestar and then adjust it "upward or downward to account for the particularities of the suit and its outcome." Id. (quotation omitted). In an order dated approximately two months later, this court granted Zinna's request for appellate attorney's fees and remanded that matter to the district court for a determination of the amount.

On remand, the district court ignored this court's mandate as to trial fees, reevaluated the Farrar factors, and concluded once again that Zinna's success was merely technical. It then refused to calculate a lodestar. Instead, the district court determined Zinna's trial counsel should only be reimbursed for an amount equal to seven hours work, at an hourly fee of $290, for each of the eight days of trial. The district court's order, dated November 8, 2012, stated: "ORDERED, that the plaintiff Michael Zinna shall recover $16,240.00 for fees incurred in this case. Because the determination of Zinna's appellant counsel fees must await further proceedings, the judgment will not be altered until that is done." On March 15, 2013, the district court entered an order explaining why it determined $18,687.50 was a reasonable appellate attorney's fee for Zinna's appeal. On the same day a judgment was entered "awarding plaintiff Michael Zinna attorney fees of $34,927.50 for legal services of trial and appellate counsel."

Zinna filed a notice of appeal on April 13, 2013, stating his intention to appeal from the November 2012 order awarding trial fees and the March 2013 order awarding appellate fees. Acting sua sponte, this court ordered the parties to brief the question of appellate jurisdiction. Specifically, the parties were directed to file memorandum briefs addressing "[w]hether Appellant's notice of appeal, filed on April 13, 2013, was timely as to the district court's November 8, 2012 award of attorney's fees." Thus, the jurisdictional question is now also before this court.

III. Discussion

A. Trial Fees

The jurisdictional issue we must address before proceeding to the merits of this appeal is whether Zinna's notice of appeal from the award of attorney's fees for the trial proceedings is timely.1 See Steel Co. v. Citizens for a Better Env't, 523 U.S. 83, 94-95, 118 S.Ct. 1003, 140 L.Ed.2d 210 (1998) (holding jurisdictional challenges are not subject to waiver or forfeiture and can be raised by the court, or a party, at any time). Pursuant to Rule 4(a)(1)(A) of the Federal Rules of Appellate Procedure, a notice of appeal in a civil case "must be filed ... within 30 days after entry of the judgment or order appealed from." Here, the district court entered an order awarding trial fees on November 8, 2012. It entered a separate judgment on March 15, 2013, covering both trial and appellate fees. If the March judgment is the final appealable order, Zinna's appeal of the trial fee award is timely because his notice of appeal was filed within thirty days of that judgment. If the November order is the final appealable order, his appeal of the trial fee award is untimely.2

An order is final if it contains "a complete act of adjudication" and evidences the district court's intention that it is the court's final act in the matter. United States v. F. & M. Schaefer Brewing Co., 356 U.S. 227, 234, 78 S.Ct. 674, 2 L.Ed.2d 721 (1958); United States v. Evans, 365 F.2d 95, 97 (10th Cir.1966) ("[I]n determining whether a judicial act is a final judgment, this court puts importance upon the intention of the judge."); see also Century 21 Real Estate Corp. v. Century 21 Real Estate, Inc., 929 F.2d 827, 830 (1st Cir.1991) (holding order awarding attorneys fees was not final because order did not set the amount). Congrove argues Zinna was required to file his notice of appeal within thirty days of the November order because that order unambiguously and conclusively settled the issue of trial fees. Zinna does not dispute that point but argues the matter before the district court on remand involved both trial and appellate fees. Thus, he argues, the unitary issue of attorney's fees was not conclusively settled until the district court awarded both trial and appellate fees on March 15, 2013.

We agree with Zinna that, under the unique circumstances of this case, the final appealable order was not entered until March 2013. When attorney's fees are recoverable by a prevailing party, issues surrounding those fees are collateral to and separate from the merits of the underlying suit. White v. N.H. Dep't of Emp't Sec., 455 U.S. 445, 451-52, 102 S.Ct. 1162, 71 L.Ed.2d 325 (1982). When an appeal is taken from a decision on trial fees, however, the issue of appellate fees related to that appeal is not itself a separate matter collateral to the issue of trial fees. Instead, the matter is properly treated as a singular appeal involving the determination of both trial and appellate fees.

The sole issue raised in Zinna's first appeal was the question of fees for trial counsel, a matter collateral to the merits of Zinna's First Amendment claims. Zinna prevailed in that appeal, the issue of trial fees was remanded to the district court, and he was awarded appellate fees with the amount to be determined by the district court. Thus Zinna's first appeal resulted in this court instructing the district court to calculate both trial and appellate attorney's fees on remand. Although that instruction was contained in two separate orders, the July 25, 2012 order awarding appellate fees was a supplement to the mandate originally issued by this court on June 27, 2012, and was docketed as such. Mandates from single appeals are not separable and, thus, the mandate in Zinna's first appeal encompassed both trial and appellate fees. The issue of attorney's fees related to Zinna's lawsuit was not fully and finally adjudicated until March 15, 2013, when the district court satisfied our singular mandate by completing the calculation of all the fees to which Zinna was entitled. See S.L. ex rel. Loof v. Upland Unified Sch. Dist., 747 F.3d 1155, 1161-62 (9th Cir.2014) ("[A] disposition is final if it contains a ... full adjudication of the issues at bar, and clearly evidences the judge's intention that it be the court's final act in the matter." (quotation omitted)). Because Zinna's notice of appeal was filed within thirty days from entry of that judgment, this court has jurisdiction over the issue of both trial and appellate fees.

Having concluded we have jurisdiction over the trial fee issue, we have no hesitation further concluding the district court acted in contravention of the law of the case doctrine when it determined Zinna was entitled to trial attorney's fees of $16,240.00. Under the law of the case doctrine, "once a court decides an issue, the same issue may not be relitigated in subsequent proceedings in the same case." Ute Indian Tribe of the Uintah & Ouray Reservation v. Utah, 114 F.3d 1513, 1520 (10th Cir.1997). "An important corollary of the doctrine, known as the `mandate rule,' provides that a district court must comply strictly with the mandate rendered by the reviewing court." Id. at 1520-21 (quotation omitted). In Zinna's first appeal, this court concluded his "victory was not merely technical." Zinna, 680 F.3d at 1242. On remand, however, the district court reached the contrary conclusion after conducting its own analysis of the Farrar factors. The court then premised its award of trial fees on its conclusion "only a technical violation" of the First Amendment was proven by Zinna at trial, failing to first calculate a lodestar as required by our mandate.

"[W]hen a case is appealed and remanded, the decision of the appellate court establishes the law of the case and ordinarily will be followed by both the trial court on remand and the appellate court in any subsequent appeal." Rohrbaugh v. Celotex Corp., 53 F.3d 1181, 1183 (10th Cir.1995). Congrove concedes the district court's fee award must be reversed unless an exception to the law of the case doctrine applies. She argues this court has the power to ignore the prior panel's opinion because it was "clearly erroneous and would work a manifest injustice." United States v. Alvarez, 142 F.3d 1243, 1247 (10th Cir.1998) (setting out three circumstances in which this court will not apply the law of the case doctrine). That exception, however, is exceedingly narrow and Congrove has failed to cite any case from this court in which it was invoked to set aside the explicit and fully reasoned decision of an earlier appeal. See id. ("[T]his panel is not an en banc panel and, thus, is not in the business of overturning prior panels' decisions.").

The district court's analysis of the trial fee issue on remand contravened the law of the case doctrine and the mandate rule. Accordingly, the court abused its discretion when it awarded Zinna trial attorney's fees of $16,240.00.

B. Appellate Fees

Although Zinna also purports to challenge the district court's award of $18,687.50 in appellate fees, the issue is mentioned only twice in his opening brief. In the summary of the argument section, he generally asserts the district court incorrectly concluded the prior appeal was simple and straightforward. In the section of his opening brief addressing the law of the case doctrine and the mandate rule, Zinna asserts "the trial court ... simply picked a number out of the air for the amount of time that should be compensated for the appellate work." Because there is no argument, authority, or record citations supporting these assertions, the appellate fee issue is not sufficiently raised on appeal. Accordingly, the issue of appellate fees is waived. See United States v. Cooper, 654 F.3d 1104, 1128 (10th Cir. 2011) ("It is well-settled that arguments inadequately briefed in the opening brief are waived." (quotation and alteration omitted)).

C. Costs

In its initial fee award dated September 24, 2010, the district court ordered the judgment entered on December 10, 2009, to be increased by "costs of $9,464.51." Neither party appealed this cost award. Although this court vacated the district court's fee order in the prior appeal, it did not disturb the cost award and the district court has, likewise, never eliminated those costs from the December 2009 judgment. Accordingly, we accept Congrove's concession that the order awarding costs remains valid and enforceable.

IV. Conclusion

We affirm the district court's judgment insofar as it awards Zinna $18,687.50 in attorney's fees for appellate proceedings in Appeal No. 10-1482. The court's judgment awarding Zinna $16,240.00 in attorney's fees for the trial proceedings is reversed and the matter remanded for further proceedings consistent with this opinion and the prior opinion of this court in Appeal No. 10-1482. Zinna's request that the matter be reassigned to a different district court judge is granted.