New Developments in Calculus of Variations
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E4: Mathematical Physics".
Deadline for manuscript submissions: 30 April 2026 | Viewed by 614
Special Issue Editors
Interests: fundamental equations of physics; foundation of variational principles; standard and non-standard Lagrangians; Lie groups and gauge field theories
Special Issue Information
Dear Colleagues,
The search for unifying concepts and general principles is one of the important goals of human beings. The most illuminating examples are variational principles that are concerned with the maximum and minimum (or, more precisely, stationary) properties of a broad range of mathematical and physical problems. The principles are characterized by an elegant mathematical structure and are known for their utility in solving numerous problems of mathematics, physics, and other areas of science, as well as important optimization problems in human life. In mathematics, the calculus of variations concerns the existence of minima, maxima, and other critical values of a real-value functional. In theoretical physics, Lagrangian formalism, resulting from the variational principle, is central to any classical or quantum theory of particles, waves, or fields. The most fundamental equations of modern physics are derived from Lagrangians that are typically obtained by solving the inverse problem of the calculus of variations. Variational principles are also known in chemistry and geology and have also entered biology and some social sciences. Variational methods in optimization are commonly known and applied in engineering, economy, business management, and financial markets.
The purpose of this Special Issue is to gather a collection of articles reflecting the latest developments in the following areas: the calculus of variations and its inverse problems; Helmhotz conditions and their generalization; variational methods in differential equations; variational methods in optimization; Lagrangian formalism with its standard and non-standard Lagrangians, null Lagrangians, and gauge functions; invariance in Lagrangians; gauge and Lie groups; gauge theories and variational principles; variational symmetries; gauge systems with Grassmann variables; Lagrangian interactions; classical and quantum dynamical systems; applications in mathematical physics; and others.
Prof. Dr. Zdzislaw E. Musielak
Dr. Rupam Das
Guest Editors
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Keywords
- variational principles
- Lagrangian formalism
- standard, non-standard, and null Lagrangians
- Lie groups and symmetries
- conservation laws
- classical and quantum dynamical systems
- optimization methods
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