Global markets breathed a sigh of relief this morning, as Greece's new Prime Minister was sworn into office on a mandate to implement a $177 billion European bailout and impose austerity measures on Greek society. The Dow Jones industrial average opened up 175 points, with the S&P 500 and Nasdaq following suit with 1.4 percent and 1.2 percent gains respectively. With the fate of the euro zone in the balance, Papademos, formerly a banker and European Central Bank vice president. will need satisfy both EU austerity hawks and disgruntled Greek citizens. Here are the key features of this juggling act:

He'll have European elites on his side Vassilis Monastiriotis, a senior lecturer at the London School of Economics tells CNN Papademos is "well versed in Greece's financial and political systems and is well respected by economists, Greece's politicians and European leaders ... Papademos has the advantage of a well defined assignment -- ratifying the October 26 bailout agreement and passing the legislation to implement it."

Elite support could work against him, though Harold Meyerson at The American Prospect notes that Papademos has never held elective office or served as a minister or sub-minister of any kind in the country. His support primarly from outsiders could work against him at home. "Imagine if the U.S. couldn’t sell its Treasury notes (which has never been a problem, let’s be clear), and the International Monetary Fund and Germany and China got together and said that Barack Obama, Joe Biden, the Cabinet and the Congress had to go. Imagine that they then designated as Obama’s successor, say, the guy who followed Tim Geithner as head of the New York Fed (I don’t even know who that is), or Robert Zoellick, the American who heads the World Bank. That’s essentially what just happened."

He'll have competing forces at home Time's Joanna Kakissis says Greece's party leaders and disgruntled citizenry will be too major problems. "Most Greeks want to stay in the euro zone although they're balking at the austerity measures Greece's creditors have demanded. Papademos' biggest challenge is trying to convince Parliament to approve further belt-tightening when people clearly don't want it," she writes. "Many worry more cutbacks will only exacerbate the social unrest that has plagued Greece since its first round of austerity measures 18 months ago, while others say the 64-year-old doesn't have the savvy to handle both Greek politicians and antiausterity protesters, who have accused him of engineering a 'financial coup' to assume leadership of the country."

It will likely be a bumpy road ahead for Europe and Greece Speaking to CNN Money, David Jones, chief market strategist at IG Markets said the "small bounce back" in the markets this morning shows there is some optimism that Papademos will be succesful. "The problem with this crisis is that almost every few days we get a fresh shock," he said. "I don't think by any stretch we've seen the worst of this. There's more volatility to come."