Eigenvalues of Laplace and Schrà  dinger operators play a fundamental role in many applications in mathematics and physics. This graduate-level book is devoted to their qualitative and quantitative mathematical analysis. It assumes no prior knowledge in this area and leads up to cutting-edge research on sharp constants in Liebà â â Thirring inequalities.
Eigenvalues of Laplace and Schrà  dinger operators play a fundamental role in many applications in mathematics and physics. This graduate-level book is devoted to their qualitative and quantitative mathematical analysis. It assumes no prior knowledge in this area and leads up to cutting-edge research on sharp constants in Liebà â â Thirring inequalities.
Rupert L. Frank holds a chair in applied mathematics at LMU Munich and is doing research primarily in analysis and mathematical physics. He is an invited speaker at the 2022 International Congress of Mathematics.
Inhaltsangabe
Overview; Part I. Background Material: 1. Elements of operator theory; 2. Elements of Sobolev space theory; Part II. The Laplace and Schrödinger Operators: 3. The Laplacian on a domain; 4. The Schrödinger operator; Part III. Sharp Constants in Lieb Thirring Inequalities:5. Sharp Lieb Thirring inequalities; 6. Sharp Lieb Thirring inequalities in higher dimensions; 7. More on sharp Lieb Thirring inequalities; 8. More on the Lieb Thirring constants; References; Index.
Overview; Part I. Background Material: 1. Elements of operator theory; 2. Elements of Sobolev space theory; Part II. The Laplace and Schrödinger Operators: 3. The Laplacian on a domain; 4. The Schrödinger operator; Part III. Sharp Constants in Lieb Thirring Inequalities:5. Sharp Lieb Thirring inequalities; 6. Sharp Lieb Thirring inequalities in higher dimensions; 7. More on sharp Lieb Thirring inequalities; 8. More on the Lieb Thirring constants; References; Index.
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