Singular Perturbation Problem in Boundary/Fractional Combustion

Motivated by a nonlocal free boundary problem, we study uniform properties of solutions to a singular perturbation problem for a boundary-reaction-diffusion equation, where the reaction term is of combustion type. This boundary problem is related to the fractional Laplacian. After an optimal uniform H\"older regularity is shown, we pass to the limit to study the free boundary problem it leads to

Competing to Cut Carbon: State Policies, Conflicts with Federally-Regulated Energy Markets, and recommendations

Wholesale power markets currently face challenges from changes in federal regulations and advancements in technology, which have significantly changed the composition of energy generation sources across the United States over the last two decades. States have relied increasingly on policy to increase the presence of clean energy sources in their power mix, such as nuclear energy, due to its reliability and environmental benefits. Natural gas, wind, and solar have seen unprecedented growth in the last five years due to declining fuel source and technology costs. Utilities companies and private companies have invested significantly in infrastructure and technology research, attempting to find success in the ever-changing wholesale power markets. Part I of this Note will provide background on federal and state regulation of the energy industry, focusing on key pieces of federal legislation, FERC orders, and technological advancements in the energy sector. Part II will provide an overview of the nuclear energy industry and the wholesale power markets in which New York and Illinois operate. Part II will also provide an overview of the state programs intended to incentivize nuclear power. Part III will discuss FERC authority over wholesale power markets, U.S. Supreme Court precedent, and recent case law regarding the New York and Illinois nuclear subsidy programs. Part III will also discuss recent proposals addressing potential market distortions from these programs and conclude that successful integration of federal and state goals in regulating energy markets requires careful coordination and implementation