Four years after Sandy, the gains in home prices on Nassau County’s South Shore have outpaced the rise in housing values across Long Island, defying some residents’ fears that the storm-ravaged region might never recover.

Along the southern coast of Nassau, homes sold for a median price of $439,000 in the July-through-September period, the brokerage Douglas Elliman and the Manhattan-based appraisal firm Miller Samuel are due to report Thursday. That’s a 4.3 percent gain from a year ago, and 12.6 percent higher than the median price four years ago, right before Sandy hit.

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“It took a while for people to not be afraid to live there, but people have short memories,” said Dottie Herman, chief executive of Douglas Elliman.

By contrast, the median price throughout Long Island, excluding the East End, was $405,000 in the most recent quarter — a 3.8 percent year-over-year rise, and 11 percent higher than four years ago.

In the Hamptons, the median price fell by 13.2 percent annually, to $825,000, as more buyers purchased homes for less than $1 million. On the North Fork, the median price was $515,000, roughly even with a year earlier.

For homes on Nassau’s South Shore, buyers pay a premium of $34,000 compared with Long Island as a whole, excluding the East End — up from $25,000 right before the storm, and just $5,000 in the third quarter of 2013, a year after the Oct. 29, 2012 storm.

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It’s a premium Jordan Weiselberg is willing to pay, to live close to his friends and relatives — and near the water — in Long Beach.

The 30-year-old teacher grew up in Long Beach. He and his wife Lauren recently put in a bid for a two-family home listed at $459,000.

Living one block from the bay will be “a mix of scary and exciting,” he said. “Although the storm is still fresh in everybody’s memories, you’re still going to have people who want to be on the beach.”

That enduring demand for coastal homes prompted Great Neck resident Allen Nathan and his business partner, Michael Sheena, to purchase a bank-owned, oceanfront house in Long Beach for $550,000 two years ago. The investors gutted the two-family house, spending more than $600,000 to add a wall of glass folding doors overlooking the ocean, a large deck and other high-end features, Nathan said. They are asking $1.395 million.

The storm actually has increased Long Beach’s appeal, Nathan said. With its many rebuilt homes, and a new boardwalk, he said, “Now when you go in the summertime it’s a completely different place.”

Indeed, many of the homes being sold on Nassau’s South Shore have been rebuilt — in many cases, elevated above flood levels — and are fetching higher prices than their more modest, street-level neighbors.

On the Nassau South Shore, the highest-priced homes are gaining in value much faster than the lowest-priced homes, said Jonathan Miller, chief executive of Miller Samuel.

But even street-level homes are finding buyers. In fact, many seniors seek out those homes because they dread stairs, said Joyce Coletti, a real estate agent with Douglas Elliman.

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“People are even buying ranches now that are not elevated, you can’t keep them on the market,” Coletti said. “People forget. In time, they forget.”